Twitter represents a fantastic opportunity if you're an organisation with a competition to promote. The potential for exposure to a wider audience of entrants is substantial, but there are a number of rules to be aware of.
Firstly, be aware of the fact that Twitter places the onus entirely on you, the competition promoter/organiser, to include an entry rule that states the creation of multiple accounts (in order to get multiple entries) is prohibited.
Anyone found doing this usually gets all their Twitter accounts suspended anyway, but the responsibility is yours to communicate that entries using this method are not permitted.
You also need to make sure you don't set rather silly competition targets - such as "whoever retweets this the most will win". That's actually Twitter's own example of a repeated tweet violation, and whilst it might surprise you there are people that think of such blatant ways of getting competition support to boost their Twitter account visibility.
Next, they state that entries on Twitter should use the Mention or @Reply method. That is, they should name you in the tweet. So, if it was a tweet to a competition we were running, your tweet would have to say "@SMT_UK here's my entry".
They also ask that you keep any conversation related to the entry relevant to it. That's a way of saying they shouldn't be asked to promote other things you do when entering, or add irrelevant hashtags to entries.
You're also obliged to ensure your competition is legal to begin with. Whilst that might sound somewhat obvious you'd be surprised how many people come up with ideas for competition prizes or methods of entry that would be illegal!
Techniques for greater exposure
There are a few very simple things you can do to get greater exposure for your competition. To begin with don't forget the thousands (hundreds of thousands, in fact) of "compers". That's people that enter competitions continuously - some even make a living out of it.
By using the hashtags of #comp and #win your initial promotion of the competition will attract a mass of such entries. You'll also find that the "compers" are likely to publish details of your competition elsewhere. There are a lot of competition-centric websites that will have its details in no time at all because a "comper" will tell them about it.
You do have to be careful though - because there's a big difference between a quantity of entrants becoming followers or a much lesser quantity becoming quality followers.
As most competitions have the intention of raising visibility, we wouldn't worry too much about the above.
Mention the word "prize" within your competition tweets.
Oh and don't forget to tweet if it's open to entrants in your home country only. The last thing you want are 5,000 entries to sift out from Germany if it's a UK only competition.
Finally, and presuming you're a business promoting a competition, you need to be on the right side of Twitter when it comes to adhering to their general business account guidelines. Don't breach their rules - because if you do you'll find your competition can lead to the complete suspension of an account.