Will having an expansion tank on the hot water pipe cause any problems?
The only 'problem' is that it fills with hot water. The water sits there and will get cold if not being used.

When the hot water is turned on again, this cooler water will mix with your hot water.

Your hot water will change in temperature a bit until the water in the tank, and the metal of the tank get hot.

Nothing will happen that will ruin your plumbing.