Are MOOCs a good way to show grad schools that I've gained proficiency in a field which is not my major?
There are several issues with MOOCs, all of which make them a poor substitute for actual classes for admissions.


Poor penetration. There is more widespread knowledge of them than a couple years ago, but they are still fairly unknown. Chances are high at at least someone reading your application won't know about or understand them.
No grades. Few MOOCs offer anything more than a certificate of completion, and many don't even offer that. Even if they offered grades, verification of identity is a problem.
Wildly varying quality. College classes are generally of a certain quality/difficulty, and knowledge of the quality/difficulty levels for certain field-specific classes across schools is something that application committees will use to judge candidates against each other. MOOCs are much more of an unknown.