The Comedy of Errors requires a bit more of the suspension of disbelief than some of the other Shakespearean comedies I've read. The idea that two sets of identical twin brothers (one set the masters, the other the servants) should run around a town for a day confusing each other, the townspeople, and one set's family members and servants is quite ridiculous. That assumes that their clothing was identical and that they all spoke the same language, with the same accent, even though two were from Ephesus and two from Syracuse. Not to mention, the unlikely accident that both sets of twins were given the same names--Antipholus and Dromio. That said, it was a very fun read, especially after all the Henry plays!
While the play had a lot to say about family and identity, it also, less obviously, added to the nature/nurture debate and, I think, comes down on the nurture side. Egeon and Emilia, husband and wife, and parents to twin boys with twin servant boys, were both shipwrecked. Fate would have it that each parent lashed themselves to a spar with one of each twin. Egeon and his set ended up in Syracuse while Emilia was separated from hers. When the play opens, the adult Antipholus and Dromio of Syracuse have been searching for their counterparts and have become separated from Egeon, who arrives in Ephesus to find them. (Needless to say, all the important family members are now in Ephesus, the home of the other A & D, and the place in which Emilia has lived as an Abbess, unbeknownst to her two).
The adult Ephesian Antipholus is a womanizer who makes his wife Adriana miserable with his absences. He also seems to regularly abuse his servant Dromio, who is engaged to a large cook in the household. Syracusan Antipholus seems more amenable to a solid marriage--he speaks of his love for Luciana, Adriana's sister: "I am thee: Thee will I love and with thee lead my life". Luciana thinks he's acting true to character, however, because she mistakes him for his brother. Also, this A. allows Dromio to tease him and treats him more like a friend, at least until the craziness of their situation intensifies. Also, this Dromio finds his brother's fiance grotesque and over-powering. The main difference between both sets of twins is that one set had a father and the other set was "orphaned" with their mother missing. That and the Syracusans knew they had missing twin brothers.
This is definitely a play I'd enjoy seeing staged, though again, I would be curious about how believable it would seem.