For instance when I pick my fighter from the hangar at the beginning it will fly out of the hangar and then just kinda float and be stuck there. If I alt tab delete and then bring the game back up it will have progressed to the next area but after enough times when the mission is loaded the screen is black and I can only hear sounds.

Video showing the issue:
https://www.youtube.com/watch?v=MYdtAXPm-kM

Any ideas on what the problem is?

I have a 120hz monitor, GTX 980, Windows 7 - 64bit.

Quite right, same problem.

Bump, bump. Have not found a solution.

Same issue here.

Contact Support and remember there's a refund policy if they can't help you out. Maybe something in this thread is relevant? http://www.gog.com/forum/star_wars_rogue_squadron_3d/cant_access_the_game_menu_after_the_intro_black_screen

Not interested in a refund, as long as GoG fixes this eventually or provides a way to fix it myself.

Speaking about fixing, I'm used to GoG games working perfectly so in case of issues like this how long do they usually take to patch it?

Unfortunately, they're probably swamped with tickets and preparing more releases, to boot. So don't get your hopes up. It doesn't help that, in over 15 years of playing this game, I've never seen this bug O.O

Apparently this is because I had turned off V-Sync, it works perfectly with V-Sync on.

Edit: If someone could mark this as the solution that would be nice.

I just found out this too, and was going to post here to tell you all, but you solved it 11 hours ago. Oh well, good you got it fixed anyway.