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?