They tend to be low on contrast, but that can be bumped. Sharpness is a bit of an issue - they usually are fixed aperture, so an f8 is only f8. However, because of their long focal lengths and the optical design, then have an even smaller depth of field than a refracting (standard) lens of the same aperture and focal length. Couple that with the fact that they are long focal lengths (i.e. prone to shake) and there are a lot of threads talking about how terrible they are. They aren't - they are mostly just a lot harder to use than equivalent refracting lenses. I was careful to say "mostly" though, as they do have slightly worse optical quality than standard lenses, and people who don't like doughnut bokeh-rings
really don't like them!
I've used a couple (Tamron and Sigma versions) and have found them fun and got some nice pics out of them. Get a good one though - the sigma 600mm is pretty good, as are any of the tamrons. Tokina are hit and miss, some people like the Mir, and the Rokinon/Samyang seem to be hit and miss.
A couple of pics from the sigma:
Shuttle take off. This was early afternoon in the summer, 12 miles (!) from the launchpad, so the shimmering/out of focusness is down to the atmosphere and not the lens' fault
Later in flight. This is looking through less of the lower atmosphere, so there's less turbulence. It's at about 35,000 ft by this point.
And a non-shuttle pic! Living the american dream