In the past year I've witnessed squirrels carrying around:
a whole tomato
a whole white-corn tortilla chip
the front panel of a brown paper grocery bag (crumpled into a ball that the poor thing had to keep stopping to re-crumple with tiny hands)
Here are some other things that squirrels probably shouldn't eat or carry around.
Prints, cards, iPhone & laptop skins, t-shirts, etc:[link]