Witchfinder General said:
I've started my wife on the show and three episodes in and she's not all that enthralled.
That's a much more common occurrence than you might think due to the show's slow-burn nature and the high level of detail it delves into. The first few episodes basically start you off right in the thick of things and both plot and character developments are done in subtle, meticulous ways, so some simply lose patience if it isn't interesting to them.
Some may also be turned off by the language, not necessarily the swearing, but the slang. Many (especially those outside of the U.S.) seem to have issues with understanding a lot of what is being said by both the cops and the gangs. I would say try to pinpoint what your wife's issues with the show so far are and see if you can clear up possible plot confusion or whatnot, if that's the obstacle. Everyone I've convinced to keep watching ended up adoring it by the end of the first season; people who dislike The Wire are typically the ones who can't get past the first few eps.