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1.
"Crossed wires" can describe either of these situations:

1. when people who are supposedly having a conversation with each other are actually talking about completely different things

2. when a dialogue gets out of sync because people are not listening to each other - in a written dialogue this is usually because someone has posted twice before reading a reply.

The expression derives from ye olden days of analogue telephones. Sometimes when speaking on the phone in the 60s or 70s it was possible to hear another conversation on the same line. You might also pick up the phone and find that instead of a dial tone you could hear a conversation. This situation was called "crossed wires".
Example 1:
Emma: I can't wait for the weekend
Joe: Freedom at last! Next year I'm going travelling
Emma: We're throwing a party for our graduation
Joe: I'm gonna hitchhike around Europe
Emma: Everyone is invited. Hope they all come.
Joe: London Paris and Rome here I come!
Emma: You are coming aren't you?
Joe: Wanna come with me?
Emma: Crossed wires!

Example 2:
Jack: I'm sick and tired of arguing
Anna: sorry I didn't mean to upset you. I forgot that you don't like talking about politics
Jack: and I get the feeling you're trying to upset me!
Jack: sorry crossed wires
by Jules Fox April 07, 2013