For a year now, I have had my own twitter account, and let me just say, for social interaction, twitter is one of the best sites. It can do everything that Facebook can do (e.g. share photos and other media, links), within a 140-character limit; however, there are some minor issues.
Twitter is like one huge conversation: use an @username to 'mention' someone, and reply to something that person said. What happens is that you can either choose to protect your tweets when you sign up, and control who 'follows' (gets a realtime feed of your tweets) you, or make all your tweets public, so everything that you or your child posts is viewable worldwide to all visitors of the site, even non-members.
Safety, however, is only a light issue. If, for example, you are a parent and your child decides to ask for a Twitter account, unless you trust your child and/or he or she is about 13 or older, it would be advisable to protect their tweets. This prevents vulnerabilities for cyber-bullying and/or hacking (password stealing).
Bad language and/or sexual themes.
Unfortunately for Parents, Twitter does not control what content users post. This means that, unless you monitor your child whilst he/she is using Twitter, they could post anything on there from personal information to revealing photographs (e.g. photos of themselves, friends, or relatives). If your child is not highly skilled with the internet, it could well be the case that they don't have (i.e. Parental Controls on Windows) or don't know how to access photo-sharing capabilities over Twitter. After all, it isn't natively supported; you have to sign up for certain websites such as TwitPic. But I assure you, I have seen swearing and sexual themes in Twitter - although it's common sense, really. All social networks (or at least most) aren't going to control user-generated content.
Again, user-generated content. People are obviously going to tweet about products, like tweeting, "Wow! I just got my iPad 2 first! Take that @twitteruser109 !" Spam is another thing... I can't count how many of my followers just post spam and advertising constantly.
Although, there are pros...
Obviously, not all Twitter accounts are going to be bad. Some are actually quite educational! For example, Oxford University have set up a Twitter account with daily quotes from C.S. Lewis. I know a lot of 'fact a day' Twitter accounts.
And Twitter is technically classed as a Microblogging service. Here in the UK, a study was conducted to see if blogging could increase the number of 5as (the British equivalent of 'A' grades) in SATs English (SATs are British tests that every eleven year old takes at the end of Year 6 (or 5th Grade in the US)) tests. The results showed that regular blogging increased the 5a numbers by up to 83%. Imagine if your child signed up for Twitter and posted blog posts (using a special online Twitter service that allows you to post tweets bigger than 140-characters). They may become straight-A students doing things they love! And learning from play is the best way to learn.
Sources: Speaking from experience. And I am eleven. And my parents did not type this.
Oh yeah, and in the UK, we have tests that 15-16 year olds take at the end of school called GCSEs. I am a frequent blogger, and I did a practice GCSE... These are my scores:
Writing 1: A
Writing 2: C
I prove my point. Twitter is the way.