Is the report that Martin was found in the possession of women's jewelry that did not belong to him going to be admissible?
I very highly doubt it, unless the prosecuting attorney asks a question that opens the door for it. The only part of Martin's character that appears relevant to me as a legal matter may be whether he had a tendency to violence of the type in Zimmerman's account of the night. Whether or not Martin was really acting suspiciously doesn't aid Zimmerman when the charge is that he was 'depraved' with respect to strangers in the neighborhood who looked suspicious, obsessively concerned that they may be committing crimes and that they always got away, following Martin, allegedly confronting Martin, and so on.
People can yell "it's relevant." Yes, to them, but not to a court. In my opinion, in a courtroom it's not just that it would be considered more prejudicial than probative. It just wouldn't be considered relevant. The relevant character trait of Martin would be whether he's prone to violence, not whether he's prone to theft.
Hell, they should try to identify the owner of the missing jewelry and see if the theft can be tied to Martin or his FB friends.