Make sure you're not standing like Quasimodo
This seems like a no-brainer, but using a standing desk is pretty much worthless if you're still hunched over your computer -- standing, by itself, doesn't erase the strain on your back and neck.
Keep your monitor or laptop propped up at eye level to maintain optimal posture (and save your back and neck!), and try to avoid the desire to rest your arms and elbows on your desk. If you're feeling fatigued while standing, go for a little stroll around the office.
Don't peer into your neighbor's desk space
When you're standing, elevated above the desk space, it gives you a whole new view of the office, and sometimes a whole new view into Brenda's work world. Monitors, personal photos, and cat calendars are all within the eye's gaze. Resist the urge to pry! The websites Brenda visits are no one's business but her own and the NSA's, and you probably don’t want to know that much about her personal life anyway.
Don't dick around on the internet
Related to the above, but more extreme. Now that your computer is elevated above normal desk height, it's much easier for people to see what's on your screen; a small price to pay for saving your back and extending your life. This means that you should probably stay on task, and and not pull up any NSFW images or websites, unless you want them to be seen by everyone walking by. Which you might want, if you're trying to get fired, but who knows if you'll be able to snag a standing desk at your next job?