The WordPress server is probably just rejecting the adsense code because advertising (aside from their own WordAds system for some bloggers) isn't allowed on WordPress.com sites (Unless you are a $3800/mo VIP member):
AdSense, Yahoo, Chitika, TextLinkAds, and other third-party advertising is not allowed here at WordPress.com.
Quoted from: http://en.support.wordpress.com/advertising/
If advertising is important to you, I suggest looking into self-hosting your WordPress blog. You give up some protection and ease of use, but you gain things like plugins and the ability to run ads. You really just have to look at the pluses and minuses and see if it is worth the trouble to you. If you decide to self-host, there are a lot of herlpful resources here: http://wordpress.org/