Maynard... This is one that people should realize, but often don't.
HDMI - like DVI is digital. Ones and zeroes. The possiblity exists that if your run is long or a cable is bad you won't get a signal to the display. But, odds are really low on that with decent cables and a fairly short run.
Then it's all ones and zeroes. They aren't going to degrade or look worse. Cross talk is basically a non-issue. There is nothing to worry about the way you would with component, composite, s-video, or RGB. It's digital, so a digital switch will handle it perfectly - unless it sucks. If it sucks, it shouldn't work at all.
On the other hand, I wouldn't spend one penny to hook up a DVD player with HDMI output to my TV - it has component out which likely looks just as good, if not better than the digital connection. The first thing I would do is find out if I even needed any of the HDMI connections, especially from the DVD player.