What evidence is there in Act IV that Claudius is losing control of his court and his kingdom?

The famous play within the play occurs in this act. Hamlet has the players play something like the "Murder of Gonzago" which is very alike what Claudius did to his brother. After the murder scene Claudius gets flustered and says, "give me some light". I think this sets off the final elements in motion that will be the King's undoing. Hamlet inadvertently kills "the good old man" Polonius which will have major implications on Laertes, Ophelia and really all the major characters later on. Hamlet convinces his mother of Claudius's guilt which certainly takes its toll on Claudius. Despite being a snake in the grass, he does love Gertrude. By the time Hamlet is banished to England, Claudius's court is quite in disarray.