No "problems" you should be aware of necessarily, as any you could come across may or not present them as such.
Speeds: You're not going to push cast bullets as fast as their plated or jacketed counterparts due to leading in your barrel in most cases. I load 124/125 RN cast as my primary shooter in a CZ-75B 9mm, and it LOVES them. I keep the velocities below 1200fps, which I'd do anyhow... but whereas a jacketed bullet won't care if it's going 1250+ a lead one most likely will leave lead in your barrel.
Feeding: Some guns won't feed cast bullets. Problem? I guess, but the same is true of different nose profiles of jacketed bullets so this is relative.
Accuracy: In many instances you'll find certain cast loads are more or less accurate than jacketed loads. Uniformity is a little harder to maintain with cast bullets but, again like any bullet type, different guns and loads will shoot certain bullets better. This is not a "cast particular" thing.
Rifling: Supposedly polygonally rifled barrels don't like cast lead. Glocks, for instance. I don't own any poly-rifled pistols, so I can't speak personally, but I've heard people say they work fine as often as I've heard otherwise.
Porting: Don't shoot cast bullets in a ported gun, if you own one. I DO shoot cast lead in a ported 44mag (Taurus), and over time I do have to do a little extra cleaning. But it's not cut into the bore itself, unlike many types of porting. In general if your barrel is ported you should stay away.
Other than (all) that, you shouldn't have any real problems if you know how to check for proper feeding and know how to safely work up loads in a particular gun. Good luck!