What you have are two examples of so-called garden paths, sentences that are arranged to mislead your reader into making the wrong parse. In the first sentence, your reader might expect a third crime instead of a consequence:
He was convicted of murder and human trafficking and driving on an
In the second sentence, your reader might expect a third item to set aside instead of an action:
She set aside the condom and lubricant and the plastic sex toy.
The general rule is that a comma separates two independent clauses, not two verb phrases in a compound predicate, so you wouldn't write
convicted of murder, and jailed
She set aside her feelings, and turned her face away.
But a good manual of style will allow exceptions which are necessary in the opinion of a careful author. As the Chicago Manual of Style notes
Punctuation should be governed by its function, which is to make the
author's meaning clear, to promote ease of reading, and in varying
degrees to contribute to the author's style.