^July 4th falls on April 7th? Now who's inelegant?
I would dispute this one. "Let's go outside and let's go look at clouds" is just unnecessarily clunky. "Let's go outside and look at clouds" is simply eliminating the repetition of the subject. "Let's go outside to look at clouds" is a different sentence, i.e. a statement of purpose. "Why are you going outside? To look at clouds". The first one is just saying that two things happened, and not implying any purposive connection between them. In other words, I would agree that "and" as a substitute for "to" is incorrect, but that dropping the subject is what's really happening, and thus not incorrect.
It's like the difference between "I went to the store to buy paper towels" vs. "I went to the store and bought paper towels". The first sentence implies the entire purpose of going to the store was to buy paper towels. The second means that paper towels were one thing you bought and not necessarily the reason you went to the store (and there is an implied subject "I" before "bought").