I actually run two instances of WoW off of a single copy on my drive, and experienced no problems.
My setup is on a Pentium 4 3 GHz CPU with 2gigs of ram and a Radeon X1950 Pro on WinXP. I don't use any sort of external programs, and simply alt-tab back and forth between my priest and paladin.
I use a single 1280x1024 monitor, but run my WoW instances in windowed mode 1280x768. One instance is top aligned, and one instance is bottom aligned. With this arrangement, I can see the health bars and minimaps (herb and mine) of both characters while the bottom client is in the foreground. So usually I have my paladin, the tank/dps'er in the bottom window in the foreground, and the priest healbot passively following in the top window that is partially exposed in the background.
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