We have a well and recently noticed our water pump is reading 60 and does not decrease when turning the pump off. Does this indicate a leak or something?

It should hold pressure when off.

This will take several helpers but read the haguge and have someone else turn on several faucets, does the gauge drop at all?

If the gauge just stays at 60 all the time, then the gauge is bad. You can check it by using a tire gauge at the air valve at the top of the pressure tank. They should read about the same.