I think she knew exactly what happened as soon as the doctor hugged her - that Castle had seen him coming down the hall and changed what he was going to say mid-stream.
I know she knows, but she's being clueless about something. I just haven't figured out what, exactly, yet. Whether it's that she doesn't think she deserves Castle or what, I'm not quite sure, but she's being willfully obtuse.
I think that she initially thought he wasn't in the right place for her kind of relationship, but she's now in the process of changing her mind on that.
And I think Castle is going "She really digs that guy, and I don't want to cause her grief, she gets enough of that."
But wouldn't it be considered a huge no-no for the two of them to start up a romance while working together? Esposito and Laney are at least in different departments.
It might not count since he's not a cop. Dunno.
If it affects their working relationship, he can just leave, there's no job involved.
Somewhat related to Castle, I found out recently that Susan Sullivan's sister works where I work! Not that I've met her.
Not only is he not a cop, he's not on any payroll. Castle is there on a completely voluntary basis. If and when his presence, whether due to a more personal relationship with Beckett or age-related dementia, becomes more of a hindrance than a help, Beckett could ask/demand/beg that he stop the ride-along. Yes, there is a certain amount of pressure from The Mayor, but if she really did not want him there, she could get him to stay away. If and when they do become romantically involved, there will be some wrestling with the notion that his presence could jeopardize her judgment and put her in danger, or seriously jeopardize her career because he gets himself into trouble. Whether that's a short conversation and resolved like Peter Wimsey and Harriet Vane managed that conflict between them, or whether it is the theme of half a season, nobody knows but the show-runners (and maybe they don't know yet).
I hope they get a somewhat serious discussion of "Castle, you've been married twice, what do you know about making a real relationship work?" Maybe it's something Martha could bring up, she's got a remarkably sensible head on her shoulders.
I don't think that two divorces makes him less knowledgeable than someone who hasn't been married at all. It might make him more knowledgeable. It might have no bearing at all.
He'd definitely have to ask himself why his marriages didn't work. It's been intimated that the one with Alexis' mom didn't work because as much of a kid as he is, he knows when and how to be an adult, something which she still struggles with, thinking that life's the eternal party.
The one with his publisher/editor is a stickier situation, given that she's obviously an adult, so why didn't that one work? Because she's in a position of power over him? He seems to be able to deal with that where Beckett's concerned, but maybe that's because he acknowledges that she's the professional. So if it's not the actual power, maybe it's the manner in which it's wielded? Maybe it's just a case of compatible only up to a certain point?
Maybe it's because for all her independence and strength, Kate occasionally allows herself to lean on him?
So many delicious possibilities.