If a device has trouble with 1.2v cells, it has some design problems. Even an alkaline battery spends ~50% of the time under 1.2v if you discharge it fully. It's only 1.5v very briefly, the voltage falls quite rapidly under use.
So if a device won't take a 1.2v cell, realize that when you use alkalines, you're throwing the cells away with 50% of the capacity remaining. Time to find a better engineered device!
The notable things the substitution of 1.2v cells can affect: battery level indicators won't be as accurate and max speed / brightness for things like flashlights, RC cars, most things that are motor driven.
I've never run across anything that's had trouble with my rechargeables.