After Ann returns the belt to Boots, he immediately puts it on. A few scenes later, he is seen without the belt and in a later scene, he is again wearing the belt.
When Duke and Boots view the windows in the vacant house from the outside, the shades are mostly drawn. But when they enter the room the first time, the shades are mostly open.
Roger's taxi from the airport starts out as a 1959 Plymouth. The interior shot shows the rear window of a much older car. Then when it's leaving his house after dropping him off, it's a 1959 Ford.
Jerome Cowan's character describes his car as a 1954 Buick Skylark, but the car used in the film is a 1953 model (which has a slightly different design - different front hood badge and front bumper 'bullets').