Ethidium bromide and mutagenesis on cloning
Purified DNA contains negligible amounts of ethidium bromide. PCR and gel clean-up kits remove it quite well. There is, though, a risk of mutation from the fact that you're visualizing the gel in UV light with ethidium bromide. The risk of mutation from UV is minimized by exposing the gel as little as possible, and by using "preparative" transilluminators that come with a low-light setting for cloning purposes. If you work well and quickly, the chance of mutagenesis isn't higher than the chance of a polymerase incorporating the wrong nucleotide.