At my parent's house, one shower has a handle that goes from hot to
cold. You have to put the handle at one certain position to get any
hot water, and then it isn't very much. If you move the handle just a
little bit in either direction, the water is cold. (The sink in the
same bathroom gets plenty of hot water.)

My mother asked the plumber who installed it and he said that the
reason is that it is a low-flow shower head. I think that the valve
is either installed incorrectly or messed up.

What do you think it is likely to be?