I saw on TV that not all sperm are the same. Some have mutations like 2 and 3 tails? There were other mutations as well.
If one of these mutated sperm actually fertilized an egg, would the embryo be mutated in some form or fashion?
Yes, the embryo would get that DNA mutation.
Both sperm and egg are haploid, meaning they only have 1 copy of each gene. When the sperm fertilizes the egg, the resulting child is a diploid, meaning he/she has two copies of each gene. However, if the sperm was mutated, then child has one mutated copy of some gene(s).
Depending on the gene(s) that are mutated and the sequence of the mutated gene(s), this could result in non existent to severe consequences.