When the Stonecutters are singing "We do", the position of several characters, particularly the Martian and Chief Wiggum, change randomly as the camera angles change. The Martian starts at the end of the table on the right side, with Chief Wiggum two seats to the left of him. In later shots, the Martian, then Wiggum are both switched to the same position, midway up the left side. Then, when the song ends, Wiggum has disappeared, and the Martian remains in this new position.
When the Stonecutters begin "We Do", the table is clean. As they continue singing, the table becomes littered with puddles of ale. When the ribs are served immediately after they finish singing, the table is clean again.
When Homer "wins" the poker game, he joylessly proclaims himself the winner and pulls the chips over his cards; however, after the camera switches to the other players and back to him, there are no chips on his cards and they are completely different cards.
Number One states that the Stonecutters have "endeavored to shatter the stone of ignorance", yet, in "We Do", the members boast about keeping the world ignorant of Atlantis and Martians.
Even if Grandpa Simpson and Mr. Burns joined the Stonecutters later in life, it would still be impossible for the much-younger Number One, Lenny, Carl, and Moe to out-rank them.
The sign for "Stonecutter's Daycare" should read "Stonecutters' Daycare".