You may remember that in meiosis a process called crossover occurs, in which DNA is exchanged between homologues, or the genetic codes from the organism's parents. This is one of the reasons why we cannot end up with identical siblings (unless, of course, they are twins).
You may not have known that crossing over occurs in mitosis as well. However, it is not measurable, because sister (identical) chromosomes look the same whether or not they have crossed over.
However, in rare cases, a mistake can occur, leading to genetic abnormalities such as recessive trait spotting (like a patch of red hair on a black haired individual) or even cancer.
