When Ward and June confront Wally and Beaver about the botched haircut, Wally is lying on the living room couch and Beaver is sitting on the floor at the end of the couch. After a cut to close-up, Beaver is now sitting on the floor directly in front of Wally.
When Wally and Beaver are talking in their room, right before Wally calls Beaver a "goof", Beaver appears to be mouthing Wally's line along with him.
A couple of things make it obvious that Beaver is wearing a modified "bald cap". Its edge is slightly visible on Beaver's forehead and his temples wrinkle when he's looking in the mirror after Wally has finished cutting his hair. Also, his scalp is especially shiny.
The shot of Beaver eating soup during the introduction is taken from the previous episode. The black eye Violet Rutherford gave him is visible.