Smudgy Glass

There once was a small family named Smith. The father had to work all day, and often the mother took her kids with her to go grocery shopping on the weekends. One winter day in the middle of December, it was once again a weekend and Mrs. Smith once again had to go grocery shopping. But this time, the oldest child David (who was twelve), decided that he was old enough to stay home with the younger kids: a 3-year-old (Tim) and a 4-year-old (Jane). Anyway, Mrs. Smith agreed and went out shopping without them. The whole time, she worried and worried about her kids at home alone and finally rushed home as fast as she could. When she got home, she found her kids safe and relatively happy. She also found a whole bunch of smudgy fingerprints all over the glass windows! Mrs. Smith was not very happy about this and accused David of making them.
"I didn't do it, Mom, I swear! It was the younger kids!" David said. Unfortunately for him, his mom was no fool and had proof that he had made the smudges. What proof did she have?