The things with the OB's - it clear they were aware of Kurumi's condition, it's known at the end that the mole man is her doctor, but did he get her to that school just for the Roman Club? The OB's give them more activities than normal because Kurumi's time is so limited, but was her joining just a happy accident? Not known.
I think Hideo could have gotten more out of Kurumi and the Doctor if he had just asked, but this was alluded to in one of the later chapters when Kurumi was hospitalized and it never occurred to Hideo to just ask the front desk - Hideo never sat down and thought things through, he just acted on impulse a lot. The Doctor allowed Hideo to think of him as a rival likely because he knew it would push Hideo to try harder, work harder, and do more to demonstrate his importance to Kurumi.
The only thing I wish was in this story, was more insight into Kurumi's past. I know that the point of the story was that the past was irrelevant, the future was impossible, and the the present moment was the only absolute that was given. Still though, it would have been great if they asked more about each other and gotten to know the person that they purport to love.
Last thing: I get the Roman Club/OB virgin-pact thing, they pretty much did everything but and never really discussed their relationship... but, beyond Kyouko possibly knowing by watching and the Doctor knowing because it's his responsibility to know, no one else knew - the mother hoped - but no one knew... that was the saddest thing IMO. The reader doesn't even know if he ever told anyone afterwards the true extent of their relationship or even just what they meant to each other. Sad!