Star Trek First Contact is probably my favourite Star Trek movie however I have to admit it has flaws and I understand why certain hardcore Trek fans hate the film. If I try to be objective and say which film is the most well written I probably pick the typical Wrath Of Khan.
However because First Contact was my introduction to the Trek series and made me seek out TNG (and later on the rest of the series) it has a special place with me. I think the issue is that as an independent film disconnected to the series, First Contact is a excellent film and is for the most part internally consistent. If you never watch a single Star Trek film in your life, you can easily watch this film and enjoy it. However as a film that is connected to the franchise it may well be considered a betrayal of taking the Borg and radically changing it for the worst.
Problems with the film
1) The actions of the Borg in the film are inconsistent of their motivation that was established in the series.
Borg sees people as resources and are purely interested in acquiring knowledge and acquiring technology. Assimilation was a means to the end. Why would they be interested in going back in time to assimilate earth when they have primitive technology and will not gain anything from it? Humanity was really no threat to the Borg survival and there is no desperate need for them to wipe out humanity. They only attack the Federation because they want their resources and time travel undermined that. If they really want to have this plot, then they should have gave a logical reason for the Borg to go back in time such as Federation developed a weapon that could wipe out the Borg and hence their survival is at stake and have to go back in time and assimilate them before they can deploy that weapon. As it is though it is present in the film, their motivation is completely contradictory. Also a question has to be ask that if the Borg were able to time travel. Why don't they just time travel when they were a lengthy distance from Earth and then travel and take over an undefended Earth? Why they have to go all the trouble in combating the Federation fleet when they can bypass them completely?
Now as an independent film this is fine, bad guys who want to go back in time to enslave the human race, which is perfectly fine. However connected to the series this is problematic and I don't think this is a minor nitpicking error
2) The Borg Queen undermine the whole premise of the Borg
The Best Of Both Worlds episode presented the Borg as this cold, emotionless monolithic species where there is no such thing as individual and free will as all the individuals that make up the Borg are part of the collective whole. This was what made them such a threat that many minds together are greater than the sum of its part (but also their weakness that the main characters expose). Every individual of the Borg are just part of the whole. There was Locutus who was the spokeman for the Borg but it was clear that he wasn't speaking as an individual but speaking in behalf of the Borg as a whole and he remained cold and emotionless.
Now what happen in this film is that we have the Borg Queen who is behaving very as an individual, also instead of the robotic communication that Locutus has in TNG, she behaves quite emotionally throughout the film. Then not only that she tries to seduce Data. Is there anything more antithetical to the Borg than sex? Not only that when she dies, the entire Borg crew dies. Essentially the Borg was weaken and neutered where before every single individuals are just part of the whole to now where they behave under chess rules where you just kill the leader and everyone dies. This is one major retcon of the Borg and essentially undermines what made them such a big threat. IMO First Contact was the film that started the trend of weakening the Borg as a villain until they became a joke in Star Trek Voyager.
Now as an independent film disconnected to the series this isn't that much of an issue. We have a dictator (the borg queen) enslaving the entire collective to behave on her behalf. There's nothing intrinsically wrong with that but it's not the Borg. although I will say even as an independent film, the idea of the borg queen trying to seduce Data was pretty weird and a bad scene of the movie.
3) Picard's character arc is contradictory
This critique actually applies to the film as an independent film as well rather than just continuity error.
The problem is that the movie has two contradictory message about Picard
Picard was so scarred by his assimilation that he wanted revenge and was fueled with bloodlust that override his compassion. In fact Lily used that as an argument against him about him killing Ensign Lynch, he was able to gun down a Borg and screaming and enjoying killing the Borg even though they were member of his own crew instead of trying to save them like the crew tried to save Picard when he was assimilated.
However how can Lily tell Picard off for not trying to save the crew on one hand and then on the other hand tell him to blow up the ship killing everyone on board including crewmembers who were assimilated. It seems a little bit hypocritical of her to do that.
If the movie wanted to stay consistent with that message, I would suggest the movie would have improved if they have the crew found a way to destroy the Borg ability to communicate and enforced their control over the collective (hence liberate all the individuals who were assimilated). However that plan is incredibly dangerous and that it would be easier to just wiped out the Borg. Essentially instead of risking getting the win-win scenario, Picard decided to play it safe and blow up the ship and kill all the Borg out of bloodlust and Lily has to convince him to find compassion and overcome his desire for revenge.
This is because I believe in a film about how Picard was so blinded by bloodlust and fueled with revenge, it seems like him blowing up the ship and killing all the Borg would have granted his revenge.
If they really wanted to go into why Picard wanted to refuse to blow up the ship then the movie should have gone through his background on why he refuse to do that. I mean there has to be more to the situation than just simply revenge as revenge can be achieved blowing up the ship. For example if they wanted to keep that direction they should have gone through the aftermaths of the Enterprise D destruction and how he felt about that lost and how that destruction hurt him bad especially as he wasn't there to save the Enterprise and wondered if he was on the Enterprise D perhaps it would have never been destroyed. Perhaps even bring up the Stargazer and how when that was destroyed he was scrutinised by a overzealous lawyer and how that left a sore spot in his career about the destruction of the ship he was captaining and how much he takes it personally. That he was so determine not to let this happen again least of all to his worst enemy the Borg.
I just don't think the whole blinded by revenge was sufficient to explain his actions.
4) Data could have ended the movie pretty early on in the film :)