One of the examples of bad design Donald Norman discusses in his seminal book The Design of Everday Objects is the door with a handle and a sign saying Push. If the door is meant to be pushed it should have a plate instead of a handle. A plate gives the affordance of pushing whilst a handle gives the affordance of pulling. Hence the need for a Push sign if the door has a handle instead of a plate.
I was reminded of this in the Lori's Diner next to the King George Hotel. Its entrance door swings both ways. Each side of the door has a handle and a Push sign.
I still can't quite decide whether that's design genius or design imbecility.