When the police sketch artist finishes his drawing, we see a close-up of it, showing a detailed caricature of a frowning Muldoon. Next we see Captain Block's horror at this, and he proceeds to take it and rip it up . But the picture he destroys is of a smaller, different face.
When Toody and Muldoon are in Muldoon's car on the way to see Schnauzer, whenever the scene cuts from Muldoon to Toody and back again, the car that can be seen in back of them through the rear window--actually a rear-projection screen--keeps changing. When the camera is on Muldoon, a 1956 Cadillac can be seen through the back window. When it cuts to Toody, a 1955 Buick is seen. When it cuts back to Muldoon, we see the Cadillac again. A few seconds later it cuts back to Toody and a 1959 Ford is in back of them. A few seconds after that it cuts back to Muldoon, and there is no car at all in back of them.