Kiddushin 65: Marital Dispute

A new mishnah - with a series of cases: when there's a dispute between a man and a woman as to whether he betrothed her (and the implications of betrothal, which prohibits them to some of each other's relatives, for example). Which of them is to be believed? Or rather, how do we handle not knowing whom to believe? Also, an Amoraic dispute on at least one of the cases in the mishnah: with Rav saying the man should be forced, apparently to give a get, and Shmuel saying he should be asked to give a get.