Okay so the part where you shoot the grenade launcher at the end and it goes right through/doesn't blow up the chopper happened to me too.
But I did some searching and I found a thread on BattleLog where someone suggested to spam the Start/Menu (pause?) button as soon as you enter the quick-time event where your car is hit and Irish hands you the M320 launcher. It sounds weird, but after failing like 10-20 times on this one little glitch, this method worked for me first try. I also waited a coulple of seconds until the chopper was more steady, but I'm not sure if that makes any difference.
Hopefully this could help someone else out struggling as I was. 😕mileyhappy:
Link to BattleLog thread mentioned: http://battlelog.battlefield.com/bf4/forum/threadview/2955065228921780422/