Amidst all the other stuff mentioned, I think a big problem is the film is trying so hard in places not to do the obvious the ideas it comes up with instead wind up being not-obvious because they're terrible.
The opening Enterprise D scene is a case in point. After all, the intent here is to introduce the Next Gen crew to the wider casual audience who go see the new film every couple of years but don't pay much attention to the various TV versions. As an introduction... it's bloody awful.
You do get a rough idea of some of their characters, but there's no real clue as to what they do on the ship or what their roles in the rest of the movie will be beyond Picard's in charge. It also makes it look as if Worf is going to be a major character, before he proceeds to do nothing for the rest of the film (despite the fact his personal nemeses are the secondary baddies. Considering Worf was arguably the third most popular/recognisable character it's amazing how three of the TNG films basically waste him. It can't even be because of doing double duty on DS9 as First Contact managed to give him a decent role right in the middle of his time on that show).
The rejected original idea for the D opening of an action scene defending the observatory might have been more obvious, but you'd have quickly established what everyone on the ship does, their working relationships and had time for a bit of character establishing banter. It would also have had the advantage of being more tied to the main plot that Worf's promotion.
Also, Carson talks on the Blu Ray commentary about how expensive the sailing ship sequence was and that it ate up a surprisingly large amount of the production schedule (I think he says three out of 12 weeks, but that sounds so large he may well be misremembering, but either way it's still a lot for a five minute nothing scene). He talks with pride about how he fought to keep the sequence in the film, but frankly in this case I think the money men were right. That time and cash could have been put to much better use later in the film.
More time could have smoothed out some of the rougher direction (big honking zooms on the face of every villain as they die?) and saved money could have been better used in the final battle. No reused Bird of Prey explosion from the last film, maybe even giving the D a chance to fight a little better in her swansong. At the very least put the number of torpedoes Riker actually asks for into the stock footage...
On a more general note, I'd also have the Picard/Kirk relationship be more equal. It's odd really, TV Picard is more than capable of holding his own with Kirk and their contrasting personalities should play off each other well with each bringing something different to the partnership.
Instead (and I don't know if this is the result of Moore being too a big TOS fan or Shatner having some influence on the script) everything seems to conspire to make Kirk look awesome and Picard look completely useless and fawning.
His grief over his family's death doesn't help Picard as he's very much on the backfoot from the off, but the fact he needs to get a dead old man to come help him punch another old man in the face (with Kirk being his second choice to do this after Guinan...) just makes Picard look useless. The scale just isn't there to justify the team up of these two icons.