It's hard to know if video switching will hurt the picture quality, since this may be rather specific to the equipment and the cables you are using. However, you'd probably be on fairly safe ground saying that it doesn't improve the picture quality. As Charles noted above, you increase the chance of retaining good video quality by going directly from the DVD player to the TV monitor.
You might be interested to know that when Bryston designed their high-end SP-1 preamp/processor, they deliberately left out video switching because they found it deteriorates the audio quality. Video switching generates a lot of high frequency interference, so it's not unreasonable to conclude that it affects not only audio, but video as well. When given the choice, it makes sense to keep the signal as pure as possible and eliminate switching wherever possible.
You might be interested to know that when Bryston designed their high-end SP-1 preamp/processor, they deliberately left out video switching because they found it deteriorates the audio quality. Video switching generates a lot of high frequency interference, so it's not unreasonable to conclude that it affects not only audio, but video as well. When given the choice, it makes sense to keep the signal as pure as possible and eliminate switching wherever possible.