According to the calendar on Ed's bedroom wall, it is April 1959.
When Ed is changing the TV channel back to the cigarette ad, the picture changes a moment before he turns the knob.
The boarding house television set sits on the fireplace mantle. However this would be impossible because the mantle is only about 12 inches deep and televisions that size were a good 3 feet deep.
When Vinnie and the professor leave Ed's room, the ceiling light in background in the hallway is hanging extremely low, about even with their shoulders which would make it impossible to walk under if that hallway was real.
When Ed puts the coin in the pay phone and lifts the receiver, the entire wall holding the phone moves.