Mr. and Mrs. Smith/Headscratchers


 * So...basically, John's employer and Jane's employer both simultaneously discover that the two are married, and then the two agencies *work together* to concoct an elaborate Batman Gambit wherein the two will kill each other. Why not just call their own agent in for a "regular meeting" in some secure location and then blow the place up while they are inside it? Or, if you really want to get both of them, arrange for both of them to be in the same building at the same time (indoors, not outdoors), and blow it up.
 * That's not how these organizations work. For one thing, to just get them both in the same place and blow it up (which would be fairly sloppy as opposed to the elaborate setups and methods they're usually shown using), and would attract undue attention. When a gun smuggler gets his neck snapped in his hotel room, no one asks "Why?", when two supposedly innocent, normal community members blow up in a terrorist bombing people start asking a lot of questions. But probably a large part of it was that the organizations agreed that it was a problem the agents caused, let the agents sort it out, maybe one of them will still be left with a usable agent at the end of the day. Remember, they're given twenty-four hours to sort it out on their own (IE one of them dies at the other's hands), it's only after that the agencies put a hit out on both of them.
 * Oh, while I'm at it -- why did it take "5 or 6 years" for the employers to discover the marriage???
 * Because covering their tracks and not leaving a lot of obvious hints to their profession is what these two do for a living.