I happened to catch the episode entitled "Beaver's Short Pants" last night, and in the scene where Ward calls Beaver to the garage to give him a change of clothes, there was a quick cutscene where he went from wearing Aunt Martha's clothes to the ones Ward brought out.

I could have sworn that scene was longer when I watched it on Netflix - and sure enough, it was. Not a whole lot, but some small talk and more of showing Beaver getting dressed.

It left me wondering.....What other episodes were "butchered" and what scenes were cut?

I assume you are referring to an airing of this episode on TV, because on the DVD the episode is complete, 25 minutes and 45 seconds, nothing is missing, nothing is edited.