the end??

SPOILERS:
He eats boiled chicken with the psychic (Julie Kavner), and she fusses over him in a typical "Jewish Mother" way. There is obvious attraction, but Woody resists because of Mia Farrow waiting at home. He walks back to his flat and Mia has left him a "Dear John" letter, leaving him. There is then a cut, and we see Woody and Kavner walk on to a balcony, telling his "sky mother" that they are engaged. His mum says "Now, I approve of her", and re-materialises on his sofa. Kavner goes and sits down with her and they look through his baby pictures, while Woody looks on, happy that his mother is back down on earth, but a little bemused that he is basically going to marry a woman just like his mother.
Hope this helps. You missed maybe the last three minutes of the film.