Gordon says it's July, but as the repeatedly re-used stock footage of the Batmobile pulling up to police headquarters show, the two old ladies are wearing winter clothing.
When Batman and Robin confront Freeze in front of the Gotham Hotel, it's nighttime. However, in the next shot, a plane is skywriting across a daytime-blue sky.
Alfred pours hot tea for Batman, but Adam West inadvertently tips the cup towards the camera several times, revealing it to be completely empty.