The reference Clive gave refers to miscommunications between people, but the expression can also refer to any error you make as an individual - getting on the wrong bus, going to class on the wrong day, etc. It applies most perfectly to miswiring a piece of equipment, especially swapping the polarity.
There's also "to cross the line," which is to go beyond the imaginary bounds
In the context of marketing communications, crossing the wire refers to the time at which a press release is distributed to a list of channels. It differentiates from the time at which the release is queued to be released since press releases are scheduled ahead of time.