I'd like to write an app that would utilize dialog from a play script, but I don't want to reinvent the wheel. Is there an open format for encapsulating characters, locations, dialog, scenes, acts, etc? I was sure there must be, but all I see is references to proprietary software packages. There are the classes Shakespeare XML/DTD files, but they don't seem to have any widespread use.
Most screenplays for film and television are written and produced using FinalDraft [ wiki link ], a proprietary software.
If you're conducting research, you're most likely to find screenplays, and other document as PDF's (an Open Format). Using PDF's as a starting ground you may find yourself looking into various scraping techniques, depending on what you'd like to do with them.
Fountain.io is an MIT Licensed plain-text markup style that allows the creation of screenplays in a more open format.
The Text Encoding Initiative's XML language has a module for "Performance Texts" by which they mean plays, screenplays, and other sorts of scripts. If you're looking for very prescriptive rules, TEI will disappoint you (there's usually more than one way to do anything in TEI!), but if you want a hospitable markup language with a lot of existing scaffolding, TEI should work nicely.