DON'T DO IT ALONE
Things happen. Life happens. Work happens. Everything happens. And never at a convenient time. The last thing you want to do is have an amazing activity or contest going, and then it all fizzles because something happens and you cannot keep up with the demands. Get as much help as you need for judging, maintenance, etc. Whatever needs to be done, take your excellent idea to your friends, and ask for help - before you get started. (That way you aren't scrambling for volunteers after everything is going and an emergency happens.)

HAVE CLEAR RULES
Have clear and concise rules mapped out before you begin. Have someone read through them and look for loopholes. Do you find something that needs to be changed? If you've already posted and opened the activity or contest, you should not change them for that round. It is not fair for those who are preparing. BUT... you can chalk it up to a learning experience, and for the next round, you can change them.

MAKE THE WORK MANAGEABLE FOR YOUR OWN SCHEDULE
Only you know how much you can handle. Some activities are a lot of work over a long period of time. If you are intending to do an activity that involves daily updating of forums, gobs of emails, offline trackers, etc., make sure ahead of time that you have the necessary time and energy to put in to keep track of everything. If you do not have the sort of time necessary to manage this type of activity, but still want to do something for the community, consider donating to an existing activity or contest, or running a different activity that is not so time intensive.

BE ORGANIZED
Running a contest or activity is the worst time to "wing it". Make sure you have judges, volunteers, rules, spreadsheets, formulas... anything you might need lined up ahead of time. Including back up people, just in case those you had lined up originally have something come up and need to back out.

BE RELIABLE
If you say you're going to do something, do it. If the contest is supposed to be judged within a week of closing, then that needs to happen. Now, if there are reasons this cannot happen, communicating with those that are affected by it is usually sufficient - but the key is communication. (For example, if you are expecting between 5 - 10 entries, and receive 50, you are going to need more time to judge.)

Show that you are reliable, and you will have people entering again and again. Your contest and activity will grow in popularity and you will RULE THE WEBS... yeah, no you won't, but you will do well.

UNDERSTAND THAT NOT EVERY ROUND GOES PERFECTLY

Sometimes, there aren't many entries. Sometimes, everything falls apart. Sometimes you wish you'd never opened the contest or activity at all. Don't let it discourage you - try again. Learn from every experience. There are a million reasons it can go wrong, including being the wrong time of year, a prompt that just didn't grab people's attention, advertising that just didn't get out there - anything could have happened. Just take a deep breath, and try again.