Do you think male Soldiers should know the female regulations in AR 670-1 just as much as the female herself?

Yes

Part of being a leader is having enough knowledge to correct a subordinate's wearing of the uniform when necessary, or praise them for setting an outstanding example. I didn't wear naval aircrew wings, but some of my Marines did, so I made sure I understood all of the regulations regarding naval aircrew wings.

In the Navy, our advancement exams have a little portion that applies to regs. No matter what gender you are, you will receive questions on male and female regulations. So that's the Navy. Personally, I agree. All men and women of every branch, especially NCOs and POs, need to know the regs of the same and opposite sex. It's our job to correct them and if you fail to and a more strict Senior NCO recognizes that, they won't care if you are the opposite sex or not.

I think we should, but I admit I don't. I have to look up female uniform (mainly hair) information regularly.

Leaders should know and enforce standards I used to keep pertinate excerpts in my leader book

Absolutely. It doesn't matter male of female, all should know the regs.

All NCOs should know AR 670-1 without regard to gender. You didn't state the specific issue, such as wear of the hair, make up, nails, etc. Regardless, you know what it states, or you don't. Easy to infer someone is try to make corrections where there is no violation, which is an opportunity to educate that NCO.

I would, if I had women in my unit. When I did- I keep my mouth shut till I had looked up what was bothering me, then we talked.

Absolutely...