Think of the kids!
This is something out-of-towners often miss (heck, even locals sometimes miss it): There are kids around you (this goes for pretty much any place not named "Bourbon Street"). Mardi Gras throws, despite what you may think, are mostly for them. Be mindful of them -- that means not standing directly in front of them, snatching throws meant for them, being especially vile around them, etc. etc. Do you really need another string of cheap, plastic beads? Consider giving it away to the little ones around you instead.
Go to the bathroom beforehand.
This might just seem like practical advice, but it also prevents awkwardness later. It should go without saying that peeing on someone's lawn or cutting in line/making a mess at the few bathrooms you do find are no-no's (and they are), but desperation makes animals of us all. Go beforehand.
Keep your belongings 6 feet back.
People are split on the appropriateness of ladders, BBQ grills, tents, and other bulky items (mostly because the people who bring them often shade random passers-by for ... trying to pass by). Folks on either side of that debate need to remember to simply be kind. But keep in mind that city ordinance is to keep everything 6 feet from the curb -- so make sure you do that much at minimum.
Respect your elders.
In the same way you should be mindful of kids, you should also recognize the older set. Move aside on the sidewalk, be friendly, and try not to intercept throws meant for them either (really, try not to intercept throws meant for ANYONE, especially stuff that was clearly hand-made FOR THEM).
Don't throw things back!
You see those riders on the floats? You see how most of them are wearing masks? Yeah, they can't see so well under those things all the time, especially a string of hard plastic beads heading for their face at 30 mph. Besides, it's really, really rude.
Meeting up with friends? Whether they've camped out all night and created a barrier of chairs/ladders for YOUR use, or it's a simple non-formal gathering on a street corner, it's always impolite to show up empty-handed. Bring some food/drink for the group, offer to assist with watching kids or minding the grill, or better yet, offer to show up early/stay late to help out with the bigger stuff.