1. The only mutations that count for evolution are those in germline cells. Have him show you the papers that state there are non-germlines cells that check every base of the DNA of all germline cells for a change and destroy a germline cell if there is even one base substitution. He can't. That doesn't happen.
2. He's mistaken in saying that in sexually reproducing organisms, if a mutation occurs it has 50% chance of being passed on. Which germline cell along the path to gamete formation did the mutation occur in? That affects the probability. If it happened very early on, then the mutation could be in essentially every sperm produced by the man or every egg produced by the woman.
3. So maybe he meant the F1 offspring that received a new mutation from a parent has only a 50% chance of passing it on, because the offspring would have the mutated allele from one parent and the normal allele from the other parent. Still not correct. That applies only if the organism has a single offspring. What if it had 2 offspring? Then the probability that at least one of the offspring would have the mutation is greater than 50%. What if the organism had 20 offspring? Then the probability is far greater than 50%.
4. He wrongly speaks of mutations being diluted across generations. Has he never heard of natural selection!?!?!?!?!??!?! Generally speaking, mutations arising de novo does not occur at a fast enough pace to drive adaptive evolution, but science doesn't claim that it does. Enter natural selection. Natural selection tends to eliminate deleterious mutations and to retain and spread beneficial ones.
5. Humans have different color skin, different shaped noses, different shaped eyes, different heights, and so on. If what he said were true, then this would not be possible. Darwin's finches have different sized beaks: if what he said were true, then this would not be possible. And so on and so on.
6. Organisms that become too genetically different do become incapable of interbreeding: we call that speciation! It is part of evolution, not a problem for it.
For example, a population gets geographically split. Each of the now two populations consists of interbreeding individuals. With no gene flow between the populations, their gene pools evolve independently of each other. Once the gene pools have diverged enough, some type of reproductive barrier between the two populations will exist. Perhaps changes to proteins on sperm in one population will make it incompatible with the eggs of the population. Each population can still interbreed among itself, but if the two populations are brought together, members from the two populations could not successfully produce offspring. They would then be two different species. How is that a problem for evolution????????????????