The simple answer is that the module cannot improve the Urls beyond the example that you gave : http://bizkatalyst.com/healthcaresolutions/doctor/ctl/viewdoctorforregistered/mid/412.aspx?doc_id=del01%5Cdoc-78
I assume this Url was generated with the Url Master moduel installed.
If you would like to have Urls like this one:
http://bizkatalyst.com/healthcaresolutions/doctor/1589764
You would have to redo your module code.
Specifically : change the url for /ctl/viewdoctorforregistered from a specified control to either having the viewdoctorforregistered as the default control for the module, or create a separate module with this control as the default, if that isn't possible. This will remove the /ctl/viedoctorforregistered and the /mid/412 out of the url.
Doing this action is just a change in the DNN module configuration, and would leave you with
/healthcaresolutions/doctor?doc_id=del01%5cdoc-78
Next, change your doctor id value so that it doesn't include encoded Url characters. The reason the Url looks like this is because of the url-encoded value in the 'doc_id' value. If you decode this value, you get del01\doc-78 . You need to change this value so it doesn't include a backslash ( you could replace it with a hyphen) , and you'll get a Url like this:
/healthcaresolutions/doctor/doc_id/del01-doc--78
The reason it is being appended on the end is because the regex value that filters out items for the friendly url path detects the url-illegal backslash, and doesn't include it in the friendly url path.
Finally, if you want to remove the doc_id value then you cna change your module to look for the qureystring items based on position, rather than key. Specifically, instead of looking for Request["doc_id"] you can look for the first item in the request.querystring keys collection, and use this as your value. This would give you a value of
/healthcaresolutions/doctor/del01-doc-78
Note that none of these changes involve the module at all - they are all aimed at changing the way your DNN module is generating Urls to better formulate friendly urls.
If you were to re-write the application to do this, you might as well start including the doctor name in the Url (if that's important) so you get
/healthcaresolutions/doctor/del01-doc-78/dr-smith
Please note that the advice you have been given about search engines not being able to index urls with ? and encoded characters is outdated advice. You can do a search for somethign commong like ?threadid= or even ?tabid= and you will see millions of indexed Urls. Search engines can all crawl Urls with querystrings.