Does every person have some mutant cells in their body?

Mutants all. Cellular damage occurs all the time and biologist have measured that our body corrects these damaged areas thousands of times every second. If you count the cell that have been damaged as mutant then there are clearly thousands of mutant cells in our body at any given time. Most of these just die off or are corrected but some of them can go on and cause cancer. Our body prevents that most of time.