Navdoc,
Red dot sights can work well on 1911-style pistols. In fact, in shooting competitions where 1911s predominate and red dot sights are allowed (IPSC and NRA Bullseye), the winners all use dots.
But there are some difficulties. Pistols that shoot full-power loads either have to use the new Tasco Optima 2000 sight that mounts to the slide or a frame mount that puts the sight on a "bridge" over the slide. Bullseye pistols loaded with 185-200 grain bullets at about 800 fps sometimes use a Weaver base mounted directly to the slide.
The main advantage to using a red dot sight is that acquiring proper sight picture (dot on center mass) becomes very quick and easy. There's no need to focus on a front sight; everything appears to be in one optical plane.
Disadvantages include expense (from $50 for a cheap model to over $300, not including the mount), weight, bulk (standard holsters don't work), rain/soot/dirt on the lenses, parts breakage, dead batteries, and the illusion of shakiness because muzzle movement is more apparent.