I think Griffin's biggest contribution to the team was as Kyrie's "psychologist"; LeBron managed Kyrie on the court, while Griffin dealt with him behind-the-scenes, providing a crucial buffer before his meltdown.
I thought Griff made some pretty shrewd moves when it came to cap management; he made some very "Morey-esque" moves by trading for/grabbing filler contracts that he'd shed to increase our cap long before Morey became noteworthy for doing so. The Shump and JR trade, particularly the latter, ended up working out brilliantly (at least at first) and made Griffin look like a seer (though LeBron obviously had a lot of input there.)
I liked the acquisition of Mozgov, as we were just bleeding points in the middle, but the dispensation of 2 1st-round pics made me squeamish at the time and still does. I hated the Korver move, carelessly tossing another 1st-round pic away for an aging shorter when we should have been looking to fortify our porous defense. The Channing trade was great.
I'll never forget the article that came out though where Griffin looked back on his time as the Cavs' GM and admitted to crying in the fetal position when news of LeBron's return broke. That was such a pitiful look, and it made me a lose even more respect for him.
Ultimately you have to give the guy a hand for having a role in our only championship. I don't like some of the moves he made and his tenure in NO lends a credence to the theory that his "success" was mostly due to Grant's asset accumulation and LeBron. I at least give him credit for constantly being proactive and trying to address our ends, even if his approach was wayward at times.