I'm new here but have been a Monk fan since season one, and I think he and Natalie are very cute together. I also think that both would over time realize that sooner or later but not necessarily have a scene or even set of specific scenes where either of them would professing feelings directly. At least I do not see that as very likely to happen within the confines of the show so far, much less now in the final season. That's why I always thought if the audience did get to see the beginnings of a probable affectionate relationship between Monk and Natalie it would be something that other characters would have to notice and bring to the attention of each M/N individually.
*POTENTIAL SPOILER BELOW*
My favorite way this could have happened would have actually been around the time that Julie would be leaving for college and Natalie might be feeling sad and in need of someone to talk to but who wouldn't let this slip to Julie. I wanted this 'someone to talk to' to be Stanely Kamel's character, but sadly he has passed after leaving many great performances and memories on the show and in his life.
But since the last two seasons have stated Julie's age, it now turns out that in fact she could be leaving for college around the time Mr. Monk might have another opportunity to be reinstated the idea seems more reasonable to post now, at least I am guessing based on the title of "Mr. Monk and the Badge".
I figured that a therapy session where Natalie is seeking help in dealing with Julie's leaving for college around the time of several other possible new beginnings/endings it would be very poignant and give the viewers a real chance to see how Natalie feels about all these other new scenarios, too, for example potentially having to find a new job. I think these circumstances would lead to her discussing Mr. Monk more than she probably would have expected to when she went in, and I believe this would be something the therapist would pick up on and bring to her attention. That would probably be a wealth of funnies because having anyone tell you that you might unconsciously have a romantic attachment to your boss would elicit at least two or three "No, no, that's crazy"s at first, but having the same person then ask Natalie herself to be for a few moments VERY introspective and to think back on even just a few of all the moments M/N shippers have really adored (and could be shown as a short but sweet flashback montage) would, again in my opinion, be a great way to get her to a point to where she could acknowledge how she sees him how she would like him to see her within and outside of employer/assistant roles and, towards the upcoming Mr. Monk and the Badge outcome, think about how to deal with this. To be fair and just to both shippers and nonshippers I think that Natalie's actual acknowledging and pondering on what to do about whatever her feelings may be should take place internally, with the therapist's words being simply a visible push for her to do so. I have a feeling that Dr. Bell in particular would also obviously give helpful advice to Natalie about ways to cope with her daughter leaving for college and probably encourage her to try talking to Monk about her feelings on the subject of Julie leaving since Adrian does have his very sweet moments, and it would be nice to see an empathetic hug from M to N instead of the usual other way around for a change lol
If Natalie did indeed go to Dr. Bell, he would in addition be able to give a realistic but balanced postulation about where Adrian is in life and to thus play the role of the divided fans on the issue of whether or not Monk would ever even be able or willing to have a romantic relationship with another woman. Any therapist would of course also recognize that as he would be in the same position we as fans are, able to make suggestions but not actually have a direct say in what Natalie decides to say/do or not say/do. In my opinion, if after introspection she does see him as a possible romantic interest, she would feel conflicted about revealing this to Monk whether he does or does not get reinstated because of several of the many reasons numerous antishippers have given. Again, I think the best way to bring the possibility that Natalie might feel this way to Adrian's attention would be for another character to suggest it to him, and I think the Captain in a serious conversation about the potential implications of his reinstatment, or Randy in a moment of unknowingly thinking out loud in front of Monk and the Captain lol, would be the most fitting way to do that. Adrian's, "No, no that's crazy"s would last considerably longer than Natalie's lol and having the Captain suggest that maybe Monk should think long and hard about how he in turn sees her would be advice he'd wave away but that would be nagging at him in the back of his mind.
All of this would make for at least one, or half of one, episode's worth of BOTH Natalie and Monk acting funny/awkwardly around each other, which I would love to see and which fans could interpret in different ways, but I think rather than openly say anything, Natalie will decide to simply see what happens and that both will continue to be there for each other when the other needs someone to lean on regardless of what happens with The Badge. I think by the Best Man episode Adrian will have let his guard down just a little bit more and feel able to handle the possibility that Natalie might have romantic feelings for him and that someday sooner or later she could be a romantic interest to him as well. *POTENTIAL SPOILER FINISHED*
I am totally all for a sweet slow dance between M/N at the Captain's wedding to help him come to warmly accept the possibility lol I think that would be unbelievably adorable AND wouldn't leave either shippers/nonshippers upset since it could be seen platonically or romantically, but I would hope there's at least a little brief happy eye-gazing

I agree that after Trudy's case is solved Monk may very well be feeling lost and confused, but if he does I also am sure that Natalie will be there to help and support him through that difficult time and reassure him of his self-worth, the good things and people in his life, and that she will always be by his side. I definitely think a final Trudy dream scene would be wonderful, but I feel it should highlight the good things that Adrian feels having solved the murder and not really on what anyone hopes will happen afterwards. I think even just a dream of Trudy appearing in a place that they both know, saying Thank You Adrian, holding him, and telling him that he can wake up now and that all she wants is his happiness would be brilliant enough and very special and important.

I would like there to be at least a holding of hands down the street or a peck on the cheek between Adrian and Natalie at the very end of the last episode, where Monk doesn't ask for a wipe but just smiles, but even if the above mentinoed hope-of-a-dream-sequence is the last scene of the series I think it would still be a great send off because both leave shippers/anti-shippers, and all those who are neutral, content since an "epilogue" pairing could be possible but not required in the minds of all the happy viewers

Well, that's my two cents worth at least, or judging by the length of this thing more like two hundred pesos lol
I hope it made a few minds wander a bit and wasn't too biased.