There was a theory that came up on one of the Slate website podcasts about Serial (there are a few podcasts there) that Jay was cheating on his girlfriend Stephanie. Theory goes that Adnan told Hae, Hae was going to tell Stephanie, providing Jay with a possible motive. Not sure who put this forward, but as the series has unfolded different people from back then have apparently come out with details, so it's not a totally academic theory in that sense, not from the way they were speaking. It sounded more like an avenue that wasn't investigated.
The thing I just keep coming back to is they had so much on Jay. He told them where Hae's car was, and about the burial. What did they have on Adnan, other than that he was the most recent ex, and was a bit hazy about the events of that day. Jay's timeline was all over the place yet they appear to have made bits of it fit the phone log (after discussing the log with him) while ignoring the rest. Like his assertion that they went to one of the state parks to smoke weed that day, when according to his own timeline that just was not possible.