Disadvantages are lack of control to users who have no or little programming experience. The framework can throw a user right off! Another disadvantage is that it's a very well-known framework meaning that hackers and attackers find it easy to work around basic security - there are great plugins to make a blog almost unbreakable - again it comes down to user experience and research.
Upgrading your wordpress blog is required to use the latest plugins. Failure to do so and then installing a plugin that isn't compatible can ruin your blog (I've even seen many instances of people closing down their blogs because malicious plugins have ruin their data ... their own fault really). People also go plugin crazy which devours resources, keep it under control :)
Another disadvantage is SEO - WordPress, unless you know what you're doing, is an SEO ASSASSIN! Repeat tagging without noindex can lead to crawlers registering duplicate content time and time again - it can kill your SEO.
There aren't many disadvantages and I honestly think the advantages seriously outweigh the disadvantages.
A serious disavantage (but this goes with any Wordpress blog), is the amount of spam you will recieve. Unless you install Askimet and Growmap Anti Spambot Plugin, you'll be recieving quite a bit of unneccessary comments.