Do you need to upgrade your career areas to gain career levels? Because my guy is a level 4 lobbyist, and I have had him "working on his career" for over 4 real life hours and his level isn't moving at all.
I consider this a major issue since my woman is constantly nursing and won't work on her career.
Its like you have to choose between having kids and having a career... and if you choose the career there's no real game after they get old.

No you do not need to upgrade any areas. Does your peep work on his career much? There are also things in the Varied section of the shop that help with careers - magazines and such. I think I got my first level in a career after I left the game and went to bed for the night. It could also be that it just takes longer to progress in a career as they get higher in levels. I have one statistician who is level six, but I have praised her much when she is "working on her career" and she's been around since April 23, so it's only been a couple of days. If each level took only four hours she should be level 12. So I think it just takes longer after a certain point.

By the way, she has two children, and her husband is the same position of statistician, and he's only level 5.

Also if you bought the game on day one (April 22) did you get the updated version?