The slims are a lot less, although not immune to getting the RROD. In fact, I have fixed probably over 1500 regular XBoxes, PS3 fat and PS3 slims consoles for the red ring (or yellow light of death in the PS3's case) and have yet to have 1 360 slim come in for a red ring problem. I do see some have problems with it online and in others forums, so as I said, not immune, but rare so far.
I have seen lots of the slim 360's have crappy lasers that putz out rather soon though. About the only issue I've seen on them.
As for getting banned, that only happens on modded systems and the slim drive's aren't easily moddable so not many people modded them. You can test it in 30 seconds though, just connect to a network and run the network test in the settings menu. It will try to connect to live and banned box won't connect right at the first stage.