I am going to France using my newly approved AP.
--- When you depart US nobody will ask you for AP, you should surrender I-94 with airlines,
--- While coming to US you may have to show Original AP to Airlines before taking a flight for US (make copies of AP, Airline may ask for Copy, don’t give original)
Can someone tell me what 'difficulties' (if any) I will encounter upon re-entering the USA?
--- You will stand in the line for Visitors and show your AP, you may be taken to secondary inspection and the POE officer will check BCIS computer and will stamp your AP, keep the copy of I-485 filling receipt with you (show if asked)