I've been running a Bridgestone Exedra (like originally came on my bike) on the rear and a Dunlop 404 on the front for a little over 11,000 miles now. I've noticed no detrimental behavior or dangerous handling with this combination to date. In fact, no difference has been noticed at all.
So, if there are any no-nos as to this practice, I couldn't tell you what or why it would be so. In short, I think you'll be fine mixing tire brands as long as both tires are bias ply, or both are radial. The difference in sidewall flexing between bias ply and radials is usually given as the reason for this.
'02 VN 750
stator replaced @ 50,570 miles
forks rebuilt @ 58,900 miles
currently on third battery & sixth set of tires