Revealing mistake: The parade is supposed to take place around Christmas, but in some scenes looking down from above, we see very short shadows under the floats and people (indicating filmed during summer). At Christmas, shadows are long all day especially in Minneapolis.
Other mistake: When Howard, as TurboMan, is stuck spinning around in the sign at the end, the parade crowd disappears.
Continuity mistake: Howard arrives back at his home in a tow truck. It is obviously late in the day judging by the sun angle. In the next scenes however it is afternoon. The parade takes place in bright midday sunshine.
Other mistake: When Howard is running behind the car driven by the lady in the fur coat, he's always shown directly behind the center of the car, but when the lady looks in her side mirror (from her point of view), Howard is in the center of the mirror. In reality, she would only see a part of Howard's left side in the reflection (not his whole body).
Answer: Most likely, she decided to keep it and not want to give it to Howard which is why she put it in her mouth.