I'm posting this as a head's up for anyone else who might be impacted by this. The short version is (and I assure you there is a longer version) - the BD-P3600 will no longer play MP3s created by iTunes. It will play other MP3s.
When I first bought my player, it did - that was one of the first things I tried, since the ability to stream MP3s was one of my major reasons for purchase. Then after a couple of firmware upgrades, I tried again, and my MP3s no longer play. My entire library was created by iTunes. MP3s that I recreated using other software will play just fine.
So, for anyone having trouble playing MP3s, this may be your problem too. I hope this helps others out there that may be scratching their heads.