The crew, made of clowners and krumpers, have visited italy, hong kong, and france.

which subject-verb agreement rule is being broken in the sentence above?

The subject-verb agreement rule which is being broken in the sentence above is collective subjects functioning as a unit require singular verbs.
The collective subject the crew requires a singular verb, because it denotes a single unit. So, instead of using the verb have visited, it should have been has visited. 

By appealing to the audience's sense of humor, sympathy, pity, and even shame, as well as establishing herself as an extremely credible speaker,

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