I haven't seen FRIDAY NIGHT LIGHTS, but it seems to me from your description that FRIDAY NIGHT LIGHTS, in trying to keep its cast together and in the same scenes, had to muddy its timeline and the ages of its characters into something less defined so that the character ages wouldn't overtly contradict their ongoing presence in the show.
I'm not familiar enough with the show to say if it's a serious issue or if it's a minor concern. A writing mentor of mine once said that continuity is a tool to add a sense of myth, history and context to a story and often declared that issues like the THE X-FILES' incoherent mythos or Laurie Strode's fate or ages of characters are immaterial and irrelevant. I am personally a little more continuity aligned where I think it can be a lot of fun to look at where a fictional universe holds together and where there are gaps, and I think it's important to eventually get things consistent enough to avoid confusion. I'm not bothered that James T. Kirk seems to be working for Spacefleet / Space Central / Star Service etc. if they eventually settle on Starfleet and stick with it.
I think all shows have continuity errors, but modern shows put more effort into obscuring them. Older TV shows were often written by writers who had not necessarily seen very many of the previous episodes because watching them required special visits for a screening in an edit room. In addition, there was the expectation that episodes would be broadcast as opposed to viewed on demand where audiences might be reviewing and looking more closely. Modern shows are written with the understanding that the immediate story may be more important than avoiding contradictions, but they still try to smooth them over, sometimes with a quippy line, sometimes by having Starfleet classify two seasons of DISCOVERY.
FRINGE is a favourite show of ours that has some pretty enormous continuity discrepancies: the series premiere has John Scott trying to kill his girlfriend Olivia Dunham by running her off the road only to die in the resulting car accident; later in the season, John is revealed to have been a hero who was undercover and his attempt on Olivia's life is acknowledged (OLIVIA: "You tried to kill me!") and then gently ignored (JOHN: "No, Liv. I loved you") and never explained. We're supposed to vaguely think that John was just trying to escape in his car; we're encouraged not to remember the pilot episode too much.
We get a glimpse of an alternate universe in Season 1 and it's completely mismatched to our full view of the same alternate universe in Season 2. In Season 1, the Peter character is being hunted by a local Boston crime boss; this is forgotten. Season 2 introduces a new Fringe agent, Amy Jessup (Meghan Markle) who disappears after a cameo in her second episode.
FRINGE tried to deal with its errors with sentiment, misdirection and distance. John Scott was revisited after a long run of episodes without him and his redemption story validated Olivia. An late Season 1 episode had Peter urgently avoiding someone assumed to be the crime boss; it turned out to be somebody else and then Peter's situation was forgotten.
Nearly an entire season passed before we saw the alternate universe in detail again, letting the audience forget how it had first appeared.
Amy Jessup was glimpsed in a cameo role with the unspoken implication that she would come in and out as needed; she never came back in. In each case, the viewer was subtly encouraged to not think about something 'for now', and sometimes, 'for now' became forever, and the show tried to let the viewer forget that all this once mattered. It didn't matter anymore.
HEROES is one of those shows where its continuity failures unfortunately tore it apart. I can't get into all of HEROES' continuity issues, but the main one: characters with powers each had a strange DNA helix symbol appear on their bodies. This meant their powers came from a specific source that had branded metahumans. In addition, all metahumans' powers reflected their user's psychological makeup: Peter's empathy made him mimic other people's powers, Nathan's distance made him fly, Claire's resiliency made her invulnerable, Hiro feeling like life was passing him by made him a time traveller, etc.
The implication: everyone with powers had been genetically altered by whoever created the helix symbol and given them the genetic potential to express their innermost states via their specific superpower. The alteration may have taken place before they were born, perhaps some sort of wide population experiment.
HEROES in Season 2 features Takezo Kensei, a 17th century swordsman whose blade has the helix symbol and has the power of cellular regeneration. The indication: everyone's powers in the present day are part of an experiment to recreate Kensei's gift, likely by randomly applying his genetic factors to test subjects without their knowledge. I'm just speculating, but I suspect this was laid down by Season 1 producer Bryan Fuller who left the show before Season 2 but after seeding some arcs.
Unfortunately, HEROES lost the (implied) genetic engineering orgin story. There was never any explanation for the helix, no origin story for the powers. I suspect the issue was the writer's strike curtailing Season 2. When the show remounted for Season 3, Takezo Kensei's actor, David Anders, had limited availability. HEROES dismissed Kensei and his symbol and all the hints and clues that came with him. And so, it discarded all the origin story implied by those clues. This also meant that HEROES lost its hold on the core theme of the show: the characters' powers were an expression of the characters' internal state. Without that framework, the writers lost sight of the characters: Peter was no longer defined by empathy nor Claire by resilience, Mohinder became a mutated reptile villain for half a season, the everyman Ando got superpowers that didn't speak to who he was at all. This was a situation where continuity actually mattered and they lost it.
However, HEROES does feature one of my favourite continuity patches. Mohinder's accent was originally Indian but the creators decided, a few episodes into filming, that they wanted him to have an English accent, perhaps it would convey more authority and full command of the English language (and scientific English). Actor Sendhil Ramamurthy proceeded to have Mohinder's accent gradually shift from Indian to English over course of Episodes 2 - 4 so that the change wouldn't be too distracting. This didn't really matter, but it's funny.
One of my favourite continuity issues: the demon-killing Colt was an essential prop in SUPERNATURAL. In the fifth season, the Colt fails to kill the Devil. The Colt is not seen for the rest of the season and it's unclear: was it dropped at the battle scene and lost? In late Season 6, it's finally established that the heroes lost the Colt in Season 5 and don't know where it is. Where did it go? Why did the writers take over a season to finally follow up on its whereabouts? Why was the follow up just a halfhearted shrug as to where the Colt had gone? Why did the writers lose track of the Colt, a vital weapon? This continuity issue was confusing and distracting. This mattered.
For years, I would randomly say to my SUPERNATURAL-fan niece for no good reason whatsoever, "Say -- whatever happened to the Colt?" This refrain became so obnoxious that at one point, she and I were playing the SUPERNATURAL edition of the board game CLUE and she threw the Colt gamepiece at me in highly understandable rage.
Slider_Quinn21 actually explained this: Season 5 was intended as the final season. When the Colt failed to kill Lucifer, it became irrelevant to the series, so the showrunner didn't follow up on it. When SUPERNATURAL made it to a sixth season (and the original showrunner left), the Season 6 writers realized: they had no idea where the Colt was. It was not retrieved on camera; it was not seen for the rest of Season 5. This meant the writers could not credibly show it in the heroes possession, nor did they know how to follow up on its present location as the Season 5 episodes had left no clues. And it wasn't that important because once the Colt failed to kill the Devil, it didn't matter anymore.
However, in Season 12, the writers wanted to do a PULP FICTION-esque heist film that required an important artifact; they chose the Colt as the artifact and finally explained where it had been since Season 5. They had a reason to use it again. And then, a few episodes later, they destroyed it, after which my niece smugly phoned me and said, "I dare you to ask me what happened to the Colt from now on."
MISSION IMPOSSIBLE isn't a TV show anymore, but one thing I find hilarious is how the Impossible Missions Force never seems like the same organization in each movie. In M:I1, IMF teams are assembled by the US from civilian or espionage for individual missions and then disperse upon completion or failure, the IMF has no fixed headquarters or facilities, and outside of a mission, the IMF ceases to exist. In M:I2, the IMF is composed of individual field agents who are assinged support staff from different fields for each mission.
In MI:3, the IMF is become a secret federal agency with offices, dedicated support teams, IMF-specific training programs, a CIA-style arrangement of divisions and hierarchy, and is a full organization rather than a mission-by-mission recruitment practice. In M:I4, the IMF is a black ops agency so distant and outside federal government that the President can dissolve it in a single memo. In M:I5, the former IMF is described specifically as Ethan Hunt's team, and the IMF is reinstated at the end. In M:I6, the IMF is a covert team within the CIA consisting of Ethan Hunt and his associates.
In M:I7, the IMF is described this way: when the CIA or NSA have a mission too complex or difficult for themselves, they "leave word" with "a man" who decides whether or not he'll accept the mission, implying that the IMF is now just Ethan Hunt and his direct associates. Paradoxically, there's a scene where Ethan welcomes a new IMF agent who doesn't appear again, suggesting Ethan is just one agent among many, suggesting that the IMF is merely a conduit to reach Ethan as opposed to being Ethan's employer. Also strangely, Ethan describes the process of being recruited by the IMF: the prospective agent must approach the recruiter and that recruiter is the CIA Director.
Somehow, MISSION IMPOSSIBLE manages to make these discrepancies trivial and irrelevant. MISSION IMPOSSIBLE movies aren't about the Impossible Missions Force. It's about Ethan, and the IMF only exists to justify Ethan Hunt's missions. In five out of seven movies, Ethan has been branded a rogue agent and isn't even working for the IMF. The IMF morphs into whatever the plot needs it to be for Ethan to be a field agent supported by a small team; the IMF will also morph into an antagonist should the plot require that Ethan be a fugitive for the story. It just doesn't matter.
Do the character ages actually matter on FRIDAY NIGHT LIGHTS? I don't know. I've never seen it.