How do I change the font for an entire screenplay?
What you probably don't want to do is just Select All and hit the Font button — that will apply a new font over any existing formatting.
What you want to do is change the underlying formatting for the document. Do that by going to Document > Change Document Font.
You can also use Format > Element Styles > Modify Element Style > Normal Text and change the font. Changing the font for Normal Text will affect all other element styles based on it (meaning any of the built-in elements). This has the same effect as Change Document Font.