Antipholus of Syracuse, exploring the city, remarks that people he has never met are continually greeting him, thanking him for favors, showing him goods he has ordered, and so on. Dromio of Syracuse dashes up to him, carrying the gold that Adriana sent to free Antipholus of Ephesus from jail. This Antipholus, of course, has no idea why his servant is bringing him money and immediately asks Dromio whether there are ships in the harbor on which they can book passage out of Ephesus.
As master and slave converse, the Courtesan, at whose home Antipholus of Ephesus ate dinner, comes upon them and asks Antipholus S. for a ring that he borrowed from her during the meal. He and Dromio decide that she is a witch and flee, leaving the Courtesan convinced that he is mad. She resolves to go to Adriana's home and tell her that her husband has stolen the ring and demand repayment.
Meanwhile, Dromio of Ephesus encounters Antipholus of Ephesus in an officer's custody. His master demands to know where the money is to pay his way out of jail; Dromio, baffled, replies that he has brought the rope's end that Antipholus had earlier sent him to buy. Antipholus flies into a rage and tries to assault his slave, halting only at the sudden appearance of Adriana, Luciana, the Courtesan, and a would-be sorcerer named Doctor Pinch. The women plan to have the doctor use exorcism to cure Antipholus' supposed madness. Antipholus protests, and he argues with Adriana: she claims that he dined at home, while her husband (supported by Dromio's testimony) tells her that he was shut out of his own house. Pinch declares that both master and slave are mad, and they are bound and taken to Adriana's house; Adriana promises the officer to make good all her husband's debts. He tells her that Antipholus owes money to Angelo the goldsmith for a gold chain, and the Courtesan says that she saw Antipholus with the item; Adriana, of course, has never seen the chain. As they talk, Antipholus and Dromio of Syracuse rush in with drawn swords, and everyone else flees, mistaking them for Antipholus and Dromio of Ephesus, who, they assume, have escaped from Pinch. Remarking that even witches are afraid of swords, the Syracusan Antipholus orders his slave to take their belongings on board a ship.
The portrait of Ephesus as a place of enchantments continues through these scenes. Antipholus of Ephesus' bafflement at being hailed on the street by complete strangers leads him to comment that "sure, these are but imaginary wiles, / and Lapland sorcerers inhabit here (IV.ii.10-11)." His decision to blame "Lapland sorcerers," however, seems to mask a deeper insecurity, since his reference to "imaginary wiles" (which, in modern parlance, means "tricks of the imagination") suggests that he may be beginning to doubt his own sanity. As his sense of self erodes, his hysteria mounts and his panic at the Courtesan's rather innocuous words and subsequent decision to run around with a drawn sword suggests a man teetering on the brink of panic.
But, as the confusing events multiply and the conflicting stories offered by Antipholus of Ephesus and Adriana come into conflict (with Antipholus E.'s bad temper both obvious and understandable), even the Ephesians themselves become convinced that magic is afoot--or, rather, madness that can be cured by magic. The magic is absurd rather than sinister, however: Antipholus of Syracuse's forebodings about sorcerers and witches are realized only in the ludicrous mountebank Doctor Pinch, whose incantation ("I charge thee, Satan, housed within this man, / to yield possession to my holy prayers" [IV.iv.55-56]) reminds the audience of the blurred lines that define the setting--he offers a Christian prayer in a supposedly pre-Christian city. The character of the Doctor--who is described, somewhat oddly, as a schoolmaster and a conjurer--defines the comic tone of the play. In Shakespeare's tragedies (e.g., Macbeth, with the Weird Sisters), magic is a destructive force; here, sorcery is a hobby of schoolteachers and, ultimately, a sham.
I have written my own act wise summary of comedy of errors. Hope it will help students like me.