Don't know about singing, but I used a wireless lapel mic for speaking quite a bit. There are several cons, along with the pros listed earlier in the thread.
The one we used was pretty finicky about the type of batteries we used. Also, once the batteries started to weaken there was liable to be a squeal set in. Also, be careful about frequencies. They are supposed to be guarded pretty well, but atmospheric skips do happen. I have heard cell phone calls, c.b. radio transmissions, and there is the possibility that another wireless transmitter with the same freq. being in the vacinity.
As mentioned earlier, they are sensitive, so they pick up everything, and that can be embarassing, if not just distracting. Cough buttons are okay, but the whole thing about being mobile is that sometimes you would be far away from the foot pedal when you needed it. Reaching up and moving the mic with your hand causes even more noise. The solution would be a really fast and clairvoyant sound board operator.
They allow for more flexibility, that's for sure. But to me, from an aesthetics point of view, they make you look like a NASA ground controller on a lunch break.
Basically comes down to making a list and seeing whether pro or con has more entries. Also, how critical is your mobility? The more you need to move, the more valuable they become.
Just take them off before proceeding to the little boys or girls room.