Having Ellis call his father would probably help on that front.

I thought maybe it meant she DID like coffee.

There was a point where he asked if her if she wanted coffee, she said no, and he gave a weird look.
So I wondered if his Adeline didn't like coffee, either.
I don't want the world. I just want your half.

Yeah, the ending was way too easy. And it's weird he was so quick to believe her. I'd have thought she was suffering from a blow to her noggin after the accident. And when her daughter came, I would have assumed the "daughter" was getting senile or something believing Jenny was her mom.
Also, as far as the father's realization that Jenny was really his Adeline, I felt like that was too easy, too. Based solely on how she looks and the scar on her hand, he suddenly jumped to the impossible conclusion that this woman hadn't aged a day since he knew her decades ago? That's a little far-fetched to be accepted so easily. They should have shown him noticing more things about her that were just like Adeline, first. Like any of the little idiosyncrasies Adeline must have hadSuch as an odd allergy she might have or the unusual way she eats her food or likes her eggs, etc. That would have been more believable.
That said, I still really enjoyed the movie.

At that point in the movie you don't know what his character is thinking in the hospital. He might think she's nuts, but is humoring her until the concussion wears off. Maybe it's only after the daughter and his father corroborate the story that he starts to actually believe.
I pretend to believe my fiance all the time, knowing that the truth will come out soon enough. Better to let it slide now than have an unnecessary fight.

Yes. The only way to make it more believable was to have the father (Harrison Ford) back up her story afterward. The filmmakers rushed to end the storyand it hurt the film.
"Don't get chumpatized!" - The King of Kong: A Fistful of Quarters (2007)

I might agree with you, but for one crucial exception.
Remember that Ellis had just seen a very strange series of events occur revolving around Adaline and his father. Having seen his father's reaction on seeing her, having seen how he went on about her, and the interaction after she leaves when Ellis is preparing to go after her, I think there was enough there to let him know that it was entirely possible that this woman was far older than she seemed to be.
Add to that her incredible knowledge and worldliness, some of the stories she had told, and what would surely have seemed to him as an "old soul", I don't think it's hard to believe at all. And then an obviously elderly woman comes into the room who looks twice Adaline's age, but is her daughter? Either it's a very well done, very well-scripted ruse, or it's the truth.
You're makin' me beat up
GRASS!

Yep. My thoughts exactly the same. I mean in a real situation, I'd be like, I'm dating a crazy.

Agreed.

Agreed. They were lazy and totally skimmed over that "conversation" and expected us to believe that Ellis would accept that she's immortal without ANY doubts. Ooookayyy.

it's like she was channelling her, no?