Why mutations in genes involved in general processes like DNA repair increase the risk of developing specific types of cancer?
I can't fault @WYSIWYG for mentioning the cited Vogelstein article in providing an answer. You point to what seems like a great explanation for why certain cancers arise in some tissues but not others. However, for those who look closely this paper has some serious errors in its derivation of the model, and for good reason it has come under strong fire in the last couple of months.

See this for a really important rebuttal:
http://ameyer.me/science/2015/01/02/vogel.html

Unfortunately, the paper provides an elegantly specious explanation for, in part, the longstanding paradox of why cancers more readily arise in some tissues like the intestines and from seemingly identical mechanisms, but do not seem to arise in other tissues. My favorite example, though @El Cid you do list some good ones, are inactivating BRCA1 mutations which normally play a role in repairing double stranded DNA breaks. And yet even when mutated in the germline this only seems to increase cancer risk in the breast, and really only in one gender (females).

So the answer is still quite certainly that the field does not understand this paradox, and the cited Vogelstein paper was a total tragedy of a publication. There have been a number of officially submitted critiques of the paper and the Vogelstein lab has been trying to defend it as best they can. This is however a great example of how big name labs can seem to get anything published in Cell/Nature/Science.

Another thing to consider and @El Cid points to a good example, is the pRb mutations (in a very central tumor suppressor pathway for all cells) cause retinoblastoma and not for instance intestinal or blood cancers very readily, and the retina is not a rapidly dividing tissue. So the Vogelstein paper cannot explain this.