I don't know if they do, but I think that they should.
The variety of experiences (good and bad) seems to suggest that some staff could do with some additional training. Deploying a mystery shopper would allow some 'official' reporting of crew delivering both great and poor service to customers.

However, I think that the question really comes down the crew feedback and performance management process. Does this actually happen? Most companies that I have worked for use an open or anonymous feedback process which is filtered back to management during pay review time. Those that perform well are rewarded accordingly; those that need improvement are provided with coaching and training.

I really think that BA needs to focus on providing a consistent service to passengers. I've had two recent experiences where, in the same cabin on the same flight, I've had amazing crew members, and then downright rude ones. It shouldn't be like that.