I'm a southpaw and shooting right handed guns doesn't bother me a bit. Agree with Lloyd about M16's though. Never enjoyed hot brass in my sleeve or others hot brass hitting me in the face and neck. Hot powder residue could be problem for your eyes at times too. Remington 1100's seemed to do that alot more than other guns. The only other guns that are a bit troublesome to me are bolt guns. Trying to smoothly get off a quick second shot using a right handed bolt gun is kind of comical to watch. I hate reaching across my face to manipulate the bolt. Had to do it for years though and it never occurred to me what a PIA the whole rigamorrow is until I bought my first left handed Winchester Mod 70. Now I really don't like using right handed bolt guns.
I messed with a true left handed double once. It was totally awkward. I did not like using the reverse top lever. It just didn't feel right.