How come on the main quest I finish Diplomatic Immunity and it is completely impossible to start the next quest. I have tried redoing the whole quest multiple times.

Right. This, I think is the game breaking bug people have been talking about.

One of the first major bugs, I know beth will have to fix.

If you are console, I can't help.

For PC, you can try advancing the stage: http://www.uesp.net/wiki/Skyrim:Diplomatic_Immunity

Do you think that they actually will? I play on the 360.

When the nasty FormID bug hit in Oblivion, this was fixed for all versions. That's the best assurance I can give.