They'd have a hard job PROVING that still photo's were taken during the play, rather than during a staged photoshoot of the actors on stage, in costume... I'd say you're on pretty safe ground with stills. If you're REALLY worried, get the actors to move around the stage as they would, but NOT speak any of the lines, and photograph that!

Videoing the play would be an obvious no-no. However if you're interested in shooting the PRODUCTION of the play, then short extracts could probably fall under fair use. Shooting from the wings, and keeping the sections of the play to a few seconds, while cutting it with other material would give you stronger argument here.