A couple of times in the past few weeks, after putting the car in drive and getting off the brake pedal (on a level surface), the car did not start inching forwards as it normally would. I had to give gas to get the car to begin moving. Another time on a very slight incline, the car rolled backwards (while in drive) after I took my foot off the brake pedal.
This seems abnormal for an AT and I am wondering whether it is a no biggie or whether I should have the transmission checked.

 

i think its just a messed up idle speed thing. My friend had a lincon towncar and after getting of the highway, the ECU woun't forget the uped idle speed so he would be idling at 40. Go to the dealership and ask them to take a look at it

 

I don't think anything sounds particularly wrong. While not a TL, my wifes Honda Odyssey is exactly the same way. It idles low enough so as not to cause any "pull" while stopped. I can't say how the auto TLs are since I have the MT but some of the autos that I have driven pulled at idle and others didn't. I have always overwhelmingly preferred the ones that do not pull. They are IMHO easier to drive and stay cooler in traffic since the torque converter is not continually making heat since it is fighting your braking.

Simply put you are giving it gas to make it go and stepping on the brakes to keep it still. Nothing sounds wrong with that.

 

My 06 5AT TL inches forward when idle...