Are these missing images found in your Media Library ie. did you upload them from your computer onto WordPress.com servers?
And, if so, then are they still in the Media Library? Please check.
Or are the missing images ones you have linked to on some other server somewhere else online such as flickr or photobucket that allow hotlinking?
Or are the missing images ones you have linked to on some other server somewhere else online that does not allow hotlinking?
For troubleshooting images tips see > http://en.support.wordpress.com/images/troubleshooting-images/
Is your browser version up to date? You can upgrade any browser version here. http://browsehappy.com
Note: If you are using an IE9 browser in compatibility mode that makes it render as IE7 and IE7 is not supported. To disable see > http://www.sevenforums.com/tutorials/1196-internet-explorer-compatibility-view-turn-off.html
If you are running one of the browsers and versions listed at http://browsehappy.com please do these four things:
1. Try clearing your browser’s cache: http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=32050
2. Make sure that you have third-party cookies enabled: http://en.support.wordpress.com/third-party-cookies/
3. Try with all browser extensions or add-ons temporarily disabled.
4. Try enabling HTTPS: http://en.support.wordpress.com/https/
Please tell us exactly which browser (and version of it) you’re using by checking here if necessary http://www.whatbrowser.org/ and also post any error reports you get.