I use the sbt command ~testQuick. That continuously recompiles scala files as soon as they're saved and reruns only the unittest(s) that are affected by the change.

For running my app I use the revolver plugin that offers the same thing: as soon as I save a file it is compiled and the app is restarted. When I use the Play framework this is supported out of the box: I save my file and refresh in the browser and see the changes.

This works very well.