I ended up on a WDL 146 during a daft weekend trip across France, they'd been brought in to operate a Strasbourg to Toulouse for Hop! - they'd already sent the scheduled Jota ARJ sub out on another flight as they're stupidly short of crew. I found them to be perfectly professional despite the obviously elderly 146 (I had D-AWUE).
This is amusing given that it all ended safely - however if airlines (BA are indeed part of this group) checked boarding passes at the door upon boarding they'd pick up on any mistakes like this surely. It would be interesting to know whether the screw up was in BA ops or WDL ops but I suspect we'll never find out.
If you look at what they covered yesterday it was a DUS-LCY-EDI-LCY-DUS shift, so it's entirely possible that they'd been given a similar schedule for today, or maybe assumed that was what they were operating? Like I say I doubt we'll ever find out.