TeachMe
Being long retired and no longer connected with the business of flying aeroplanes perhaps I could offer some guidance to you.
As you may well appreciate the use of flaps and slats increases the maximum capability of a wing to generate lift at a given speed. The snag is the difference in the lift potential between a ‘clean wing’ and one with high lift devices selected out (a ‘dirty’ wing) varies considerably from aircraft type to type and so it is not possible to generalise about the degree of difficulty that a particular aircraft will have in staying airborne when it is (say) clean but being flown at dirty speeds.
The situation is made even more variable by whether you are talking about devices on the leading edge of the wing or the trailing edge (or both).
The final complicating factor is that should the aircraft enter the stall regime (because the wing is in the wrong configuration for the speed being flown) then with some types this can be relatively benign – amounting to just a lot of shuddering and shaking - while on others really abrupt effects occur such as a sudden uncontrollable change in bank angle.
Your query about how often such incorrect configurations are flown is a very tricky one. For obvious reasons if a mistake is made and got away with the crew are unlikely to tell everybody and may even tell nobody. However my gut feeling is that it does not happen very often because most modern types have a warning system to alert the crew if a takeoff is attempted in the wrong configuration and when landing there may well be enough height in hand to recover the situation if the stall is approached.
As you say human factors affect us all every day (although a few very experienced and talented people may be in denial about that) and while the chances of certain critical mistakes going undetected can be reduced by crew selection and training plus better aircraft design, they can only be eliminated by the use of automation and removing man from the loop.
Speaking personally I can remember a day back in the mid 60s when I was working on the development of the first autoland system proposed for an airliner. The automatics did brilliantly and landed the aircraft in cross wind conditions that were beyond my skill level. From that day onwards I have believed that automatics are better at flying than me.
So, for me, the issue is not how well automatics can ‘fly’ but how reliable they are. Which is a totally different issue. I must stop now because my wife wants me to extract her biro from my pencil sharpener.