I've never had stains from microwaved popcorn.
But you could try vinegar.
http://www.onegoodthingbyjillee.com/2012/06/how-to-clean-and-shine-your-microwave.html
"Pour one cup vinegar (into a 2-cup measuring cup or bowl) then add one cup of hot water to that.
Place measuring cup (or bowl) in the microwave, set your timer for approximately 10 minutes and turn it on.
After 5-10 minutes (this will depend on how powerful your microwave is)
CAREFULLY remove the cup with the HOT liquid (use an oven mitt!) and wipe out the inside with a wet rag.
A Caution: If youre worried about explosions over superheated liquid, you can virtually eliminate the possibility of it happening to you by simply leaving some non-metallic object (such as a wooden spoon or stir stick) in the cup or bowl when you boil liquids in your microwave. It may not be necessary, but it wont hurt anything either."