What should someone do when they see an officer disrespecting soldiers?

Tell your Sr. NCO. 1SG preferably.

I once made a comment (jokingly with funny intentions) that a Jr enlisted in my team did not appreciate. He told my Sr NCO who then told me. Immediately I went to the soldier with my Sr. NCO to apologize to him because he was right regardless of my intentions.

This may not be the situation you are in. The take away is to talk to your Sr. NCO. Make sure it is legit.

Fill out a http://www.blackfive.net/files/hurt-feelings-report-da_form_imt_wf1.pdfhurt feelings report if your first line leaders on the NCO side don't back you up.

Well, for me personally, i would take the Officer aside and let them know exactly how they screwed up. Basic counseling stuff like they were a brand-new Airman; this is the standard (respect and dignity for all), this is what you did (acted extremely unprofessionally) and this is the delta (you have now LOST the ability to lead that human). The officer corps, be it CGO or FGO, need mentoring by the SNCOs that have been in a while. Our perspective is different, and they might not see what they are doing and how it is screwed up. And at the end of the day, what is the O going to do to me, get pissed? I'm right, I've been yelled at before so I don't care, and unless you have 3 stars at a minimum on your shoulder, you don't have the authority to demote me anyway. So stop being a dick to my Airmen...sir.

ADDED: Oh yeah, it's also in AFI 36-2618 that it is no-shit my job to do this, so if I don't then i am actually not fulfilling my responsibilities as a SNCO. No need to cuss at them (though very satisfying at times) to get the point across, either.