Laggy.
Loading screens take anywhere from 5-40 mins, depending on game.
Ease of access to friends list/complicated system.
Some games don't have much freedom on what maps ya can play on/what you can do etc online.
That's the general issues that I see/are brought up often. Of course, that's comparing it to other systems.
They're basically stone age online wise. But it makes sense as most of their games were made for SP/local in mind.