If Tumors have lots of mutations in them how is it the immune system can't detect them?
This is a good question and it gets to the most basic foundations of immunology. Your immune system is made to be flexible - able to adapt to almost any challenge. However, with so much flexibility comes the potential to generate immune cells that react against the 'self'. So, at the other extreme, the immune system needs to be limited.

In order to meet these two (potentially conflicting) goals, immune (at least lymphocytes) cells have a two-step development pathway. In the first step, the body randomizes its immune receptor specificity. In the second step, it ensures that these receptors are not auto-reactive.

Doing so means that immune cells are aware of their environment at the time that they are 'born.' Take a look at this review from the Fuentes-Panana lab to read about how tumors actively cultivate the immune system of their host in order to maintain a more favorable environment.