Wrong: She hated going to the dentist, and cried the whole way there.
Why: There's a comma between the two components of a compound predicate.
Right: She hated going to the dentist and cried the whole way there.
Why: In a sentence composed of a single subject ("she") and two predicate verbs ("hated" and "cried"), the verbs separated by a conjunction (like "and," "but" or "or"), there is no comma before (or after) the conjunction unless the subject appears a second time. If the subject does also appear in front of the second verb, you have a compound sentence, which requires a comma before the conjunction (She hated going to the dentist,and she cried the whole way there).
Next, while we're on the subject of compound elements …