Setting aside the 'is it romance?' question of the whole Dennis-Amy situation (which I don't subscribe to anyway), something I find quite interesting - in a 'where tf is your head at, man?' type of way - is the fact that Robby took issue with Dennis helping Amy with the farm and Theo, made a point of stressing the importance of establishing boundaries between patients and doctors... but still has no problem asking him to follow up with Duke?
And I think Robby suspects (and maybe subconsciously takes for granted?) that Dennis likely would've agreed to almost anything he asked of him - and Dennis has cannonically said he has difficulty saying no to Robby! Now, to what extent he was being genuinely truthful with that statement, I don't know - but Dennis said those words, he put that out there into the ether! So he at least has some self awareness to acknowledge this particular element of his behaviour with regards to Robby - again, interesting.
It's particularly interesting to me because - knowing what we do about Dennis, his brand of empathy, how he overexerts himself and goes above and beyond with his need/desire to help others - of what it could mean. The implications with how the whole Amy/farm + house sitting storyline seemed to have ended(?), to me, is that Dennis will likely be paring back how involved he'll be with the Millers - potentially significantly. What's the likelihood, then, that Dennis, being who he is, in time just swaps Amy, and Theo, and the farm, with Duke? Duke, who either has the surgery but would need help for the next couple of months at least, or doesn't and likely dies within the year. So for Dennis, what might start as following up with a patient could easily turn into inserting himself into this caretaker role - it's a slippery slope for him. Because this is the same Dennis who helped Amy as Teddy was dying, then after losing Teddy, then when Theo was born, then with the farm more generally - he gets himself emotionally invested in his patients, stretches himself too thin, doesn't offer himself the same care and regard as he does others.
Add the Robby of it all to the equation, and it's a big emotionally and ethically dubious (to me) mess. Because here's your chief attending, who (in the collective two-ish months you've known him) you've seen and helped at his lowest but still somewhat idealise, who's given you the keys to his HOUSE and the wellbeing of a CLOSE FRIEND to look after, who says he TRUSTS YOU and goes out of his way to make sure YOU ONLY see the better versions of him, even though you suspect, no you know, he's not doing well - so what are you, Dennis Whitaker, first year resident EM physician who is self-sacrificing and struggles with setting boundaries, going to do?
Season 3 is currently being written, so we obviously have no idea how his storyline is going to continue in season 3 - but with what we do know about Robby's mental/emotional state and the way Gerran's been vocal about wanting Dennis to really go through it next season, this potentially leading to Dennis-angst AND tie-in with his dynamic with Robby would be *chef's kiss*! If the writers go in that direction with them, that could be really fascinating.