I should preface this by saying I haven't completed Far Cry 3 yet.
I've just rescued Keith and upon returning him to the cave I realised that I don't give a shit about any of these characters. Perhaps it's the writing or the voice acting; perhaps they're just unlikable. In fact, I find the villains Vaas and Buck much more interesting than Jason and the gang. For a game that often desperately attempts to evoke pathos from the player, this is a significant problem. A problem which I think is a result of the way the game begins:
While this is a fun montage it teaches us very little about each character, besides establishing them as a bunch of hard drinking adrenaline junkies, all of which we will soon go to extreme lengths to reunite and be expected to care about. A memorable intro no doubt, but it feels rushed in a relatively lengthy game.
Here's how I would've done it:
Cut out all the bullshit. The drinking on the beach, kicking the coconut tree, riding the jet ski; cut it. Instead, the story picks up in a small plane en route to the jump point. Everyone is high fiving and shit just like on the beach only in this scenario we'd actually learn something about each character. When the plane reaches the jump point they jump out, in order of least to most important character to the narrative, Jason and in turn us, the player.
This is just off the top of my head. I'm sure it isn't the best intro, but it's better than what we got. Here's hoping the second half of the game improves.