Keep an eye on entries

If you want to be sure what entries are published within your contest use pre-moderation mode. Then only entries approved by you will go live.

But for contests where submission and voting round go together then better if users can upload and share entries right away, without waiting on your action. Then you can enable entries to go public right after upload (in photo competition it would take no more than 2 minutes until the application would prepare scaled photos for display).
As admin you can always jump into your contest and find out if there are new entries and if there is something wrong with them go to admin area and remove them. But it might be inconvenient, especially if there are only few new entries a day.

How to get noticed about new entries? 

You can use RSS feed, which is available at least for admins. Log in to administration, choose the current contest and go to the tab RSS feed. There you have RSS feed with latest entries. Use this feed to get updates from it directly to your email inbox. There are few applications that enable this. I’ve found and tested:
Paste here latest entries RSS feed address (copied in Competizer administration) and your email. You will get email from them with a confirmation link. Once you confirm you will be notieced about new entries within an hour about new entries in your contest.