David Deutsch has a paper called "Three experimental implications of the Everett interpretation". I can't find it online, unfortunately. The experiments are infeasible with current technology, but the fact remains that many worlds makes different predictions than orthodox QM.

The basic idea is easy to grasp. Copenhagen says there are certain sorts of systems (observers, or measuring devices) that can collapse superpositions but do not themselves enter into superposed states. Many worlds says that these systems do enter into superpositions. There are possible measurements (very difficult to conduct, admittedly, given the size of these systems) that can tell us whether or not such a system is in a superposed state.