1) Jane, I didn't see dancing in the hall, but Joe I did.
2) I didn't see Jane dancing in the hall, but I did Joe.
3) I didn't see Jane dancing in the hall, but I saw Joe.

Two possibilities:

a) I saw Joe dancing in the hall
b) I saw Joe (maybe he wasn't dancing in the hall)

I think '3' is ambiguous and '1' and '2' correspond to 'a'. Is that correct?