Although the examples are in Java, you really need to take a look at the aptly-named Metrics library by Coda Hale. And here is the Scala API for it. I think it will be exactly what you need. It even supports things like partial functions and Actors and Futures.
After seeing @Randall's comment and your edit, it is clear you are looking for static analysis tools rather than what I consider "metrics." My bad. To that end, I suggest you take a look at Scalastyle, which is much better than Gangnam Style and is analogous to CheckStyle in Java. You should also look at cpd4sbt (analogous to PMD) and FindBugs (analogous to, well, FindBugs) despite the commonly reported false positives.
