I have an Uberti Walker, and although it is probably my favorite gun in my collection right now, it does have one serious problem: I can't hit the broadside of a barn from the inside with it. Specifically, it seems to shoot about two to three feet high at any given range. It's very precise in where it puts the ball, but if I want to get a hit I have to aim literally feet low.

Now I know that it's not me, I'm actually a decent pistol shot. Last time I took it out I fired it and also a bunch of .357 out of a friends' S&W, at the same range I was getting hits precisely where I aimed almost every single time. Ranges we shot at were 35 yards, 50 yards, and 100 yards. Any ideas what's going on?

YEP . Very common to shoot high . You will have to hold low in the LOW six o'clock position in close ranges out to probably 50 yrds .

Most cap and ball revolvers, especially Colt copies will hit 12-18 inches high at common pistol distances.

You have to consider the Napoleanic tactics of the day, where lines of troops stood about 100 yards away from each other.    If you take an 1847 Walker, 1860 Army, or similar military pistol of the era with period correct sights and dimensions, and shoot at a 100 yards you'll find it shoots remarkably close to point of aim.   The sights were designed to enable to shooter to engage a line of troops at 80-120 yards and they do exactly that.

For close quarter combat with an infantry pistol like the 1860 Army, or in the case of a horse pistol like a Walker or a 1st, 2nd or 3rd model Dragoon,where it was designed and intended to be carried in a pommel holster on horse back,  the assumption was the pistol would be pointed and shot at the close ranges involved, rather than aimed, so the 100 yard regulation of the sights was immaterial.