You can get a diaper rash from wearing wet diapers all the time without cleaning up and changing the diaper often enough.
For girls they can usually get a UTI or bladder infection from the stale urine in the diaper but males are less likely to get any form of bladder infections from the wet diapers.
I've worn wet diapers all day before and got a rash but never got a bladder infection or UTI from wearing the wet diaper.