How do I remove carpet tape from a painted wall?
An iron and a very sharp wallpaper removal knife.  Heat the carpet tape, zap it with some steam... do that twice in about 3-4 mins.  Wait another 3-4 mins to let the moisture soak in - longer if tape is thick.  Heat it again, zap it with steam again...

Then you need to hit it with the blade.  I have taken down 15-20 types of wallpaper and carpet tape in my own house (yes that many and no I wouldn't do it for $$).  Most will work doing it this way.  Sometimes adding vinegar (inside the iron) will help.  The key is the blade work.  Push your blade flat and fast.  If you have to dig in on the tape - then the tape hasn't absorbed the moisture to come off or maybe it embedded into the paint (soft latex).  

Heat, moisture, vinegar, sharp blade - I feel confident that it will solve 90-99% of tape/wallpaper issues.  Now the key is how many times you have to hit it with the heat, moisture, vinegar...  If you have a small area then just take your time.  

If you are like me start off really slow with the first wall looking perfect, then a couple hours later... start to chip the paint and drywall off because you are hurrying everything, cuss, smack the wall and repair the next day.