Dick Tracy is a movie of vivid cinematic art that compares to the great visual talent by the creator's of Hero. Dick Tracy is a great example of moral character and is still human enough for us to relate to. Even in the face of diverse temptations he couldn't betray his character and what he stood for. His love for Tess was virtuous; he didn't have to live with her (or sleep with her) to show his love for her. Tracy showed love and respect towards the kid by trusting him and providing good fatherly judgment by making an effort to keep him out of danger, but at the same time he didn't hide his appreciation when the kid showed up with needed assistance.
Tracy seems a little flabbergasted at Ms. Mahoney's forwardness which causes some emotional interference between him and Tess. Eventually he's able to sort out his thoughts and feelings and realizes he loves Tess (though this happens after Tess leaves him). Tracy probably let Breathless get a little too close to him. Had he recognized the effects of this temptation on his and Tess's relationship earlier he wouldn't have put himself in the predicament that makes the rest of the movie happen (to our enjoyment).
As for the last scene, I think Tracy ultimately pitied Breathless - whether or not his move was appropriate is disputable. It (this is ambiguous on purpose) could have been more of a thank you, because she ultimately brought Tess back and helped get rid of Big Boy; or it could have displayed some true emotions he might have actually had for Ms. Mahoney.
Either way, this is a classic show with a good message. By today's standards probably should be thrown in the PG-13 category as some elements are not appropriate for a younger crowd.