I have just purchased Spyglass and entered my own url to check on my backlinks. I have noticed that there are a few less links than what appears in Google Webmaster. Why is this?

We are extracting backlinks from the search engines using the "link:domain" operator. Google does not display all the backlinks to a site with that operator:

http://www.youtube.com/watch?v=TjQ2QVQpaK0

So you won't be able to see all the backlinks to a competitors' site using that method, unless you have access to their Google Webmaster Tools' account.

You can import the backlinks that you get from Google Webmaster Tools via File -> New Project: Expert options -> Import Google Webmaster backlinks.

Try adding Yahoo to your project and re-running the analysis, usually Yahoo produces more backlinks. But, once again, talking about analyzing links to your site, not the competitors' one, Google Webmaster Tools will give you more links than any other source.