Why would Miller include the note on historical accuracy at the beginning of The Crucible?

The "Note on Historical Accuracy" actually does a few interesting jobs.

Firstly it informs the reader or the director that the play has been carefully researched, and carefully located within its context: owning up, if you like, to what is artistic licence and what is based on history.

Secondly, it reminds us that the play is based on reality: and that the sort of events Miller depicts actually did occur. There's no escape from the horror of the events: you can't simply pass it off as a made-up play. For the reader of the play, the Note serves to segue the fictional world into the real one, and reminds the reader of what they have in common.

Finally, of course, the note actually resolves some of the loose ends in the story - for readers who really had to know what happened next! For this reason, I suppose, it's often included in the programme when the play is performed in the theatre.