When Mr. Burns answers the phone, his cup of cappuccino disappears from his left hand.
The mace in Mr. Burns' limo appears and disappears between shots. Additionally, the "stand" where it is resting can still be seen on the shots in which it does not appear.
In the beginning of this episode we see a huge sound amplifier on Mr.Burns house. Later on in this episode it is gone.
Burns, trying to contact Smithers, spells out the name using his phone's dialing pad and inadvertently dialing Moe's. However, Smithers' name has 8 characters (translated to 8 digits, specifically 764-84377). However, in the US, no phone number has 8 digits. For a local call, you would use 7 digits; anything after that would not register on the phone system at the time, which is why Burns' call connected.
It is implied that Mr. Burns doesn't know how to drive, however we've seen Burns behind the wheel in the past, including earlier in the season in Scenes from the Class Struggle in Springfield (1996).