First if you set 1023 instead of 1024, that shows sloppy work and bad airmanship!
If the rules say, wrong QNH settings = Fail, than that is what it means! I guess it is up to the discretion of the examiner to see if you pick up on your mistake fast enough yourself. I would though think if you was flying around with the wrong QNH for over 20 minutes, he would not be happy with you, simply because you should have checked your altimeters QNH setting during this time (FREDA check).
Now there is no excuse that you have not spoken to the ATC, or they haven't told you an update. If you are flying from say Stapleford to Manston, and during this time you pay attention to other ATC traffic, and they suddenly give somebody a QNH of say 1025, for their region, you should be able to deduce from this background chatter on the radio, that you check and change your own QNH.
It is about being ahead of the game and following procedures.
When you go to flight school training, they teach you a set of procedures, that they know the examiners want to see on the tests, as this is a part of the CAA's examination standards!
The pressure altimeter is not going to be 100% reliable, however you would hope and think, that everybody could check first that it is set on the correct setting given by ATC, and not an own invented QNH based on apron elevation. Although this might be a more accurate QNH, is this the way your instructor have thought you, that you disregard ATC's/ATIS information, because you yourself think there is another and better way?
Where will you put the limit? If the QNH is 3mb of limits, but showing correct apron elevation, what would you use?
All make mistakes, however some mistakes are set out in the syllabus as being more serious than others.
I do not for the life of me, see any valid good reason for somebody to set the incorrect QNH with regards to your explanation here.
Why would you while on the ground, not have TIME to make sure your QNH is set correctly, but you will check it when airborne and adjust it??
What you says makes complete nonsense, there is no excuse for making this mistake, before take off the QNH is crosschecked several times, and NO it has NEVER happen to me, that I had incorrect QNH before take off.
QNH checked, altimeters within limits of each other if multiple altimeters, within limits of field elevation, situation over.
Listen to other traffic on radio during take off prep and taxi, and if any changes to QNH, I would change them automatically, without ATC needing to tell me, if in doubt, give them a quick call!
We all do mistakes from time to time, I fully agree, but this example you mention is not a good one!
When flying SEP, VFR you should normally do FREDA checks every 15 minutes, flying around on the wrong QNH just shows laziness or sloppiness in performance!
Your way of thinking on this matter is not logical from what your instructor should have thought you!