The links in the widgets may be affiliate links, or they may contain code that we cannot use on wordpress.com blogs. If so then the software will strip out the code out to preserve security on this multi-user blogging platform. http://en.support.wordpress.com/code/
If you post the code here to the forum between backticks then we can tell you what's happening. The backtick ` is found on the key to the left of the number 1 key on your keyboard. It's in lower case on the same key as the tilde ~. The format for posting code to the forum is:
You will have to post each code separately using that format.
On a sidenote: wordpress.com blogs are for posting for original content. It's not for posting duplicate content, which has been published elsewhere and which Google can penalize your blogs for.