When Paul is putting shaving cream on with the brush at the beginning of the sink scene, he lathers it on relatively thick in the frontal shot but then when the scene cut to the side shot as he begins to shave, the cream is on in a thin, uniform layer.
After he uses the butter, Paul rests alone on the floor on his left side. Next shot he appears on his back.
When Jeanne disappears during her bridal gown fitting, Tom goes running down the street to find her in the pouring rain. As he gets about fifty feet from the camera he sudden runs into a section of the street that is dry and there is no rain coming down. He apparently ran past the maximum range of the rain making equipment they were using for the shot.
When Paul monologues with his dead wife lying in bed, you can see the actress chest moving up and down at a breathing rate.
When Paul monologues with the Rosa, as he leans on her to say "Rosa, I'm sorry.", she blinks.
Brando's character does not know how to sharpen correctly a barber's razor on a leather strop. He turns over the razor for every stroke on its edge instead of its back, so blunting the edge with every stroke instead of sharpening it.
When Paul and Jeanne are at the sinks together, she says, "I prefer to be a whore." Her lips do not move during that line.
During the Tango contest scene, Paul's clapping doesn't match the soundtrack.
In the final scene, as the camera pulls away from the balcony, you can clearly see a crew member and a lighting array reflected in the glass panel of the right balcony door.
The bottle of "bourbon" is actually Jack Daniel's Tennessee Whiskey. This whiskey has all the properties of a bourbon, but since it is filtered through charcoal before being barreled, it is a Tennessee Whiskey, not a bourbon.