Copy-protected music will not play on a BlackBerry. Any songs you bought through iTunes probably has Apple's DRM (Digital Rights Management) and is thereby copy-protected. Stuff you bought on a CD and ripped into iTunes should be fine.
Media Sync sucks. Hard. Mac support for BlackBerry sucks. Hard. I've found the only way to get music onto my BB reliably is to drag and drop, directly from my Mac onto the Music folder on my mounted BB's media card.
Understand that the BlackBerry was never designed as a media player. It seems like RIM added media features almost as an afterthought so they could say, "yeah, our devices can do that too." Also, BlackBerry was never designed with Mac support in mind. They've ignored Macs until fairly recently. PocketMac works ok with older Macs, and Missing Sync works with some that don't play nice with PocketMac. In another week or two we get BlackBerry Desktop Software for Mac from RIM. I'm hoping this gives us Mac users a degree of parity with the Windows world we've only been able to get so far with hacks and work-arounds.