The only ammo related issues I know of is the use of Stingers in a Ruger match barrel. The cartridge case is longer than normal 22 LR ammo and can hit and stick in the rifling. Other than that, a standard 10-22 should run about anything you can feed it.
I have seen rifles that will have problems with hollow points catching on the edge of the chamber. Some rifles feed HP with no problems, some have issues.