Take a look at the sentence again:
During the exam, Mary sucked the ends of
her hair, chewed the top of her pencil,
and all the while she was picking at a scab
on her elbow, but she could not remember the third cause of the French Revolution.
When you list actions, you must use parallel structure. Here, sucked and chewed are both simple past tense verbs, but all the while she was picking at a scab on her elbow is a main clause, wrecking the parallelism.
To fix the sentence, change all the while she was picking to picked.