What is Miller's purpose setting this scene in a jail cell (The Crucible)?
Act III ends with a series of accusations in court. Mary can not fake fainting when she's asked so her word is called into question. Elizabeth, not knowing John has confessed to his affair with Abigail, denies that John is a lecher (that he'd committed an affair) and thereby, John's word is called into question. Hale takes John's side and when no one else (of authority) sees his point, he denounces the proceedings of the court. Everything has fallen apart and the scene ends with Danforth ordering the Marshall to take John Proctor and Giles Corey to jail.
Act IV opens in the jail. Miller chose to set this scene in the jail because Act III contained the proceedings during which those accused of witchcraft were essentially guilty before they all had a chance to defend themselves. As the proceedings devolved, more and more were sent to jail. Act III ends abruptly with Hale denouncing the entire debacle and with John Proctor going to jail. Act IV opens the following fall. Some time has passed. Therefore, those accused have spent significant time in jail. One other effect of setting the scene in the jail is that we are now removed from the outside world of the village of Salem, and it continues to spiral out of control as if it were in some other world. We learn from Hale how the village has continued to devolve and how the mass jailings have affected that outside world. Hale remarks to Danforth:
Excellency, there are orphans wandering from house to house; abandoned cattle bellow on the highroads, the stink of rotting crops hangs everywhere, and no man knows when the harlot's cry will end his life--and you wonder yet if rebellion's spoke? Better you should marvel how they do not burn your province!