Consider your motivations for seeking opinion of friend's friend
Q: I have an old, but really close friend, who has her own old, really close friend. (My friend "Jane" and I met after college; Jane met her friend during college.) Jane and I are having a fight about Jane's behavior toward me. She's got a bad temper and I think is a bit of a bully sometimes.
Meanwhile Jane's old friend "Mary" and I have been becoming better acquainted lately. We've been starting to communicate and talk outside of Jane's presence. Is it unfair to ask Mary about Jane's behavior? They are much closer — obviously, having known each other for years. But I think it would be interesting to know if Mary sees the same thing in Jane that I do. I'm not asking her to "weigh in" on our current fight, I just want to know if she's had the same experience. Mary is a sweet woman and I believe wouldn't run to Jane to tell her I've been talking to her.
Bringing Dirt to Other Parties
A: I think it's fine in an "I struggle to understand Jane sometimes, can you help me?" kind of way, but if you're not certain you can keep this out of the muck of Jane-bashing, then don't even try it.
Another way of putting it: If you want to fix your friendship with Jane, then understand that what you need to accomplish this are new ways to see the good in Jane, and Mary can help you with that. If what you want is validation for disliking this aspect of Jane, then don't even touch that with Mary.