If it ain't broke, it will be soon! No, seriously, it's a good airplane. I fly an E-90 and a C-90, which are late '70s models. They do break quite a bit. Avionics problems depend on the setup you've got.
As far as the airplane, I can't say there are recurring problems or scenarios. Only thing out of the ordinary was smoke in the cabin due to a melt-down of the vent blower fan. I hear from MX that it is fairly common for these to go out, but the smoke issue was unusual.
As far as resources on-line, I don't know of any. Come to think of it, I just saw that a book devoted to KA issues was just published.... Googling... You're in luck:
http://www.lulu.com/product/item/the-king-air-book/10668874
$50 is kinda steep, but the reviews are good. The only other recommendation I have is to get your hands on a checklist. Perhaps the Information Manual listed above will include one.
Have fun! You can PM with any specific questions. I have a close to 2000 hours in them.