fI know the person who I am getting a reference from, then they will know me and hopefully give me a honest, but more educated reference. Someone telling me "She's great, but you two would not get along" is a much better reference then "She is great."
I agree- I think that anything on my resume (or that can be figured out from it, i.e. production managers) is fair game. DEFINITELY directors, but also conductors, designers, occasionally even actors). I think it can really work to your advantage to have as much information as you can about a show listed- if a hirer knows the stage manager I ASMed for, I think it's almost expected that if they are really interested in hiring me and want information that they would call this person, even if they aren't a listed reference.
I think of this a positive, rather than negative, aspect of a resume, though. The more chance that a hirer knows someone I've worked with, the more they'll trust that person's point of view, instead of knowing that someone who is listed as a reference is undoubtedly going to say good things. Theatre is a small business, and I've definitely had hirers look at my resume during an interview and say, "Oh, you worked at _____ Theatre last season? Then you must have worked with __________, I'll have to give them a call."
Although I'm constantly reworking it, my resume is currently split into ASM and SM positions, and the headings are a little different:
Production Director Theatre/Artistic
It's chronological, since I don't have room for dates. "Production" is the title, "director" is self-explanatory, and "Theatre/Artistic" has the theatre company, as well as any other information about the show. I used to have it listed as Thetre/Conductor since I wokr in opera as well as theatre, but to take advantage of the space, I use this "artistic" heading to cover other things as well, such as listing the stage manager if I was the ASM, or if there was something that made that show stand out that I want to feature. Mostly I use it for listing conductors.
I think one of the most valuable things listed on my resume is the director- if I worked with someone that I didn't want a hirer to call I would probably leave the show off.