What're the consequences of having a cross bite?

Depends on how sever: Too many teeth in cross bite not good and should be orthodontically correct. If not can have affect on muscles of mastication and result in cracking of teeth as they are not in the position they were anatomically designed for, .

More Wear & Tear: Having a crossbite can put a lot of extra pressure onto areas of your teeth which aren't designed to function in that way. This can lead to excessive dental wear & tear, chipping, and cracking. It can also put extra stress onto your jaw joints and into your chewing muscles, which can be painful. Often it also affects facial esthetics in a negative way. Fairly easy to fix in kids, tough in adults.

Same as any other...: ...Irregularity. If teeth and jaws do not meet properly, added stress is placed on teeth, supporting bone and gum tissue, the muscles of mastication (chewing) and the jaw joints. Put teeth and jaws where they belong they function better, look better, are easier to care for, last longer, and cost less to maintain.