If he'd been arrested for something that was actually illegal they wouldn't have dropped the charges within hours. Yelling at a police officer may not be smart or polite, but it is certainly not illegal on its own.
You do have the right to yell at and berate members of the public, although it's not something I'd recommend or do. Just because it isn't OK or smart doesn't make it illegal. You particularly have the right to yell at people while on your own property, having established that you are the owner and resident and they aren't leaving once it's clear you are doing nothing wrong.

Again, I don't say what Gates did was smart or polite, but it was fully legal and there's no way he should have been arrested on charges of, essentially, attempting to start a riot.