Yes - MLBAM hosts all kinds of things. They've become very proficient at what they're good at. The only real downside I've seen is that, while they've become very good at streaming video and such services, their people aren't necessarily actually baseball fans - so they sometimes do things that a fan would never do (mess up transactions listings, etc.)
Most of the remaining video issues I've seen are hardware-related, and out at the ballparks. The Major League parks generally have good, modern equipment - the AAA and AA parks, not so much. Lots of SDTV (old analog, 4:3 ratio) cameras, etc. Reading opened the season with such a camera in center field, and with a crappy lens to boot; happily, they've now upgraded that item!