avoid the game on ps3 until it has been patched. You can't connect to games online. When you do it usually puts you in a lobby where you wait for the host to ready up but, I found this out through my account share, everyone is ready and the game just won't start. The work around has been to just add people as friends from these lobbies and start your own game but that is still a pain.
I really really like the game when it works but it just takes so much effort to get into a good game that I can't recommend it on playstation to anyone. I can whole heartedly endorse the soundtrack though, Payday 2 and Hotline Miami* are definitely my favorite soundtracks of the year.
Hopefully it gets patched soon because I have been able to have a ton of fun with the game. I believe the issue is only on playstation after checking the boards on game faqs for all three versions I didn't see any threads about it. That fact actually really bugs me since the first payday was originally a psn exclusive so the dev team should been able to make it work seamlessly.
*Yes I know it came out last year but I just got to it this year since it was released on psn.