I've been lucky with the freezes. I get the occasional 30 second pause but it always starts back up.
I've experienced several problems though:
Tattoo Bug: Showtime not only expanded the game, but it expanded this bug as well. When you go to the salon to get a tattoo, it changes your default outfit to a secondary outfit and adds a random outfit as your primary. It also adds a secondary swimsuit outfit that is identical to the one you have. This will happen every time you get a tattoo, so remember to go to a dresser and remove any excess outfits as I believe this caused a problem where my household got bugged. She would no longer automatically change into her career outfit to do her performances and would just drop the action from her cue, and the household funds wouldn't show up unless she was in build or buy mode.
Sound Bug: A lot of the time, there would be no sound while my singer was performing. This has proven to be an issue caused by an outdated sound card driver, and I can confirm that updating your drivers fixes the problem. Computer manufacturers are terrible with driver updates for peripherals, so you are often required to manually update your drivers yourself. However, I would not suggest that you do this yourself unless you're comfortable with doing it. Otherwise, ask someone who is a little more computer savvy to do it for you.
Performance/Relationship Bug: Another thing that I have noticed is that if you are performing at a venue (not playing for tips), your relationship with the audience will drop instead of increase. The better the performance, the bigger the drop. And if you talk to an audience member, they will often be "insulted." Performing for tips still works as normal.