Technically, the examples given in a couple of posts above are not parallel clauses but parallel predicates. And there’s nothing wrong syntactically with using them, though stylistically they may not work. (The classic example of this is the Time magazine compression of widely divergent information into the same sentence: “Jones, a 43-year-old bachelor and fan of Tex-Mex cooking, wrote the best-selling The Will to Succeed, and considered becoming a tennis pro in his younger years.”)
“He is tall and muscular, and works out a lot” is in no way faulty – “He,” the subject, manages two coordinated verbs and their complements: “is,” linking “He” to two descriptive adjectives, and “works out.” Because both predicates relate to his physique, they work well together. “He is tall and muscular, and wrote six novels and a history of Luxembourg” doesn’t work as well stylistically, since the coordinated predicates are not related in topic. But in terms of syntax only, it’s equally acceptable a sentence.
And while we’re dealing with connectives and style, may I throw out my own pet peeve: the run-on “therefore” sentence. “Therefore” is a conjunctive adverb, not a conjunction proper. It cannot unite two sentences in terms of syntax, though it links them logically as cause and effect. “Therefore” introducing a statement of result should nearly always be preceded by a period, or in particular unusual cases by a semicolon, and unless it introduces a very short statement should be followed by a comma.
WRONG: “The radio said the Interstate was held up by highway construction, therefore we decided to take the old road.”
RIGHT: “The radio said the Interstate was held up by highway construction**.** (or, better, “…traffic on the Interstate was held up…”) Therefore, we decided…”
“Therefore the argument is invalid” is fully acceptable; it’s extremely brief. But if the sentence grew by even a few words, a comma after “therefore” is needed.