Hello,
Which iPhone model do you have?
If you have a 7 or 7 Plus, the home button isn't a physical button. Rather it is one that uses haptic feedback. So the "wiggle" you feel may be the haptic engine being activated by your touch.
If you've got an older model, I honestly don't remember if it wiggled slightly. I'd imagine there would be a slight amount of "give" in that it's a physical button. Maybe someone who uses one of the previous models can verify if that is normal behavior or not.
Are you noticing any degradation in the function of the button?