Godzilla noticeably changes size throughout the movie. For example, she is shown lairing in a subway tunnel, but she cannot fit into the Hyde Park tunnel (taxicab scene), which is significantly larger than a subway tunnel. Also, compare the size of Godzilla's eye next to Matthew Broderick during the fish scene and Godzilla's death scene. The eye is way bigger in the latter.
Near the beginning, when Godzilla first starts his rampage, one of the assistants working at the news channel (the one talking on the phone to her mum) is the voice of Bart Simpson (Nancy Cartwright).