Capcom's Rey Jimenez has responded to bug reports for the PlayStation 3 and XBox 360 versions of Marvel vs. Capcom 2. He stated:
There's been some issues with custom match making and microphones in the PSN Marvel vs. Capcom 2. Why did these bugs show up? This is disappointing.
Rey: These major bugs are pretty disheartening to us too. I can assure you that these basic functions (like custom match and the mic issues) were tested to death during the test cycle. It's a bit confounding that these are showing up in game now when they didn't occur before. Rest assure that we are looking into the issue and that some kind of fix will be available. We're currently looking into the issues and I'll be updating everyone shortly on a course of action.
If you'd like to report any bugs you've found in Marvel vs. Capcom 2, hit this thread.
Also Saner pointed out that custom music will not work if you join a room with microphones enabled. If they're disabled when you join a room, your custom music should play.