I did that Google thing, came up with so many hits on why mismatched tyres are dangerous I went fuzzy eyed. I don't think everyone has Google accessTheres always one isnt there...
Its pretty common sense surely, its like walking down the road with 2x different shoes on. + its even illegal in some countries.
It can effect the grip levels, control ability and can various systems, eg ABS (not sure if theres any proof of this last point).
A simple Google will tell you.