Is their any way to find broken URL's?

Where the old urls built dynamically and not you are using some other way to dynamically build urls?

If that is the case, I would create vb script to watch for those patterns either on a page like

<%
theQuerystring=request.querystring

if some variable = x then
   newQstring=z
end if

' Permanent redirection
Response.Status = "301 Moved Permanently"
Response.AddHeader "Location", "http://www.mysite.com/newpage.asp?q="&newQstring
Response.End
%>

Or use pattern matching in iis 301 redirect

Otherwise you can use google webmaster tools to find all the backlinks.

i agree with padas, except I would do it at the IIS level so that you don't have to edit each page. For IIS7+, you can use the built in URL Rewriter module, otherwise there are free third party tools you can use:

IIS7 and above - http://www.iis.net/downloads/microsoft/url-rewrite

IIS 6 and below - http://www.isapirewrite.com

Google Webmaster Tools is your most direct source of missing pages that Google has detected.

Another method is to find all the backlinks to your website (e.g. Majestic SEO) and test them all to see if they are broken (e.g. Screaming Frog).

Ok you really want to use Global Redirect module for this. I would also recommend the search404 module which you can configure to either perform a search with the url parameters when a 404 page is hit, or redirect to the best match: http://drupal.org/project/search404

You can use the Global Redirect module to set up your redirects but also if you change a URL in the future, you can configure Global Redirect to automatically create a 301 redirect to the new alias: http://drupal.org/project/globalredirect

Lastly, if you are using Linux then there is the linkchecker package:
sudo apt-get install linkchecker
linkchecker -r2 --ignore-url=^mailto: --no-warnings www.yoursite.com

The -r2 is the link level to go down to, You might want to set it to -r3 or higher if there are more clicks to get to your deleted pages, although these will obviously only appear if there are links to your deleted pages.

If you're not using Linux, then you can use Xenu:
http://home.snafu.de/tilman/xenulink.html#Download

Really, the only way to do this, to find the broken URLs in Google is to use Google Webmaster tools. You will find the URLs under Crawl errors.