When Batman takes Robin (really a hollow dummy) out of the wax chamber, he seemingly forgets that he's supposed to be holding someone who weighs about 120 lbs, lifting the body with ease, and even holding it/him with one hand at times.
When Batman and Robin are back in the bat cave removing the wax from Robin, Alfred hands Robin his gloves. Burt Ward initially puts the gloves on backwards, realizes his mistake and quickly switches them. The scene never stops.
When solving the Joker's latest "clue" Robin says the "O-OH" reference is "two O's and an H - H2O - the chemical symbol for water" H2O is actually 2 H's and one O.