These things happen. Perhaps incorrect metadata, or an incorrect material ID in the playlist. You'd hope that these things get caught by the director when they're previewing things but they may be looking after multiple channels and on the rare occasion, things slip through the net.
When I worked on playout for Challenge (many many moons ago), reversions of Eggheads were being delivered inexplicably close to transmission. One day the tapes for a double bill didn't show up until minutes before TX, so we didn't have time to get it onto the playout server - merely check the timecodes and play it straight off tape. About 45 minutes later it became apparent that part two on the second tape was actually the second part of the first episode, something we only spotted because the questions were starting to sound quite familiar...
Countdown
once had the contestants and guests giving their answers to the next set of the letters instead of the ones they'd just played. It was a bit like a Two Ronnies sketch, but not as funny.
The Countdown thing is just sloppy editing, not like Channel 4 sit there playing segments out and just happened to pick the wrong one, that's an editing error.