The mathematical
ideas themselves are actually reasonably sound, the problem is in their application. In the show unfortunately, they make the problems sound a lot easier than they actually are. In many cases, for example, they're attemping to perform some statistical prediction based on a very limited set of data, or working from some prior distributions that they simply would not have access to. As a drama it's not bad, and the writers do have some interesting ideas about mathematics and analogies to more concrete ideas; from that point of view it's a reasonably good show. That said, the apparent ease with which they use these methods to solve crimes is mostly BS. Unfortunately, really good mystery shows tend to be few and far between on television.
Like using a water sprinkler and it's splash ratio to help solve crimes...
As an idea it's not really that far fetched. You
can use what you know about the splash pattern and the dynamics of the water droplets to solve the inverse problem of locating the sprinkler. However, that depends on having those models available; human behaviour on the other hand is far more complicated and is generally much less well defined. As an analogy to what was being attempted though, it was a pretty good one and explained the thrust of their solution.