I don't know that there's any way you can KNOW if his book makes valid arguments or not. The main problem is that Levitt is a good economist at a good university. So are some of his critics. How are you, as an undergraduate, supposed to know more than they do. (When people who know more than you disagree, it's hard to know who's right.)
Another reason you can't KNOW for sure if he's right is the fact that it's not always easy to know who's right in economics. You can't run controlled experiments to test hypotheses.
So what CAN you do? Assuming you're being asked to address this question in a paper/assignment, you have to look at the arguments for each side and, as best you can, tell why one argument seems more plausible to you.