The main issue re: witnesses is their credibility. So to impeach a witness there are some strict bounds on extrinsic evidence for prior acts, but with prior crimes, the rule is that you can use any felony against a witness no matter what (unless it's stale), and any misdemeanor so long as it relates to the truthfulness of a witness. IE, a misdemeanor battery wouldn't be allowed, but a theft would.

Also, after an attack like the one above on Neal would open the door to let the DA call a witness (most likely Peter) to rehabilitate Neal's reputation. At which point Peter gets to testify that Neal's reputation within the FBI is excellent and that he has a very high opinion of Neal's honesty.