What are common mistakes students make with dna profiling?
You are using the term profiling incorrectly.
Profiling itself can be misused. For example, saying that all Mexicans are drug dealers or all whites are lazy.
But as far as using a DNA profile to find out who killed someone or who is that person was who was found dead is not misusing it.
Perhaps using DNA to see if an unborn child may have genes that may cause a disease and then terminating them would fit this but many think that this use is amoral.