Or can it? I get 2 different sets of search results for deep links on my domain. One link is just the page name and the other is with the .htm extension. Backlinks are built w/o the extension but links within my domain have the .htm. Should I do a 303 to the non extension links or does it not matter?
You should absololutely use a 301 redirect or the cannonical meta tag. The fact that you are getting 2 different results means that Google is seeing your page as 2 seperate pages and sharing PR and link juice betwen them.