They are fine rifles. You can use them just fine with smokeless powder. If you're buying ammo, any standard .38 special round will work -- no +P, please. The problem isn't the brass frame -- the frame is plenty strong. The problem is the toggle link action, which doesn't really lock up the way that more modern designs do. As a result, a high pressure round can conceivably blow the bolt straight out the back of the receiver. Even with safety glasses on, that's a bad thing.
I have an 1866 in 44-40 that I load primarily with black powder, but most cowboy shooters use smokeless. Good choices are the Trail Boss mentioned by Lone Gunman, or HP38, Hodgdon's Clay's, etc.
As for common problems, there are two. The first is that there is a little tab on the back of the loading gate (aka, the "ladle"). That tab acts as a cartridge stop. On a lot of these guns, the tab breaks off, which allows cartridges to get pushed out of the mag tube get behind the gate. At that point, the gun jams up and has to be disassembled, and you'll need a new loading gate. If you are concerned about this possibility (cowboy competitors are, because it will ruin a match), then you can replace the factory ladle with an aftermarket one that is stronger. Or, you can weld the back of the tab to strengthen it. Personally, I wouldn't bother, if I was you. If yours breaks, get it fixed. The part is only about $10.
The other problem is that the mag tubes can get rust in them, and that will bind up the follower. To prevent this, be sure to clean your mag tube periodically. You have to remove the plug at the muzzle end of the tube to do so, and it can be VERY hard to remove it the first time without buggering it up, so be careful. It has a long, then slot that no screwdriver will fit just right. Some guys use the (non-sharpened) side of a hacksaw blade and get a good fit. I used a stiff putty knife on mine. If you can't get it to budge, trying soaking it in Kroil for a while.
That's brings up one more thought. Uberti uses a fairly soft steel for their screws, and they apparently have a gorilla with an impact wrench who tightens them at the factory. Far too many guys bugger up screws trying to disassemble their 1866 and 1873 rifles for the first time. Get a good set of hollow ground gunsmith screwdrivers and go slow. If you do bugger one up, you can get replacements cheaply from VTI Gun Parts.
