Comparing the provided table to the periodic table we find the following differences:
If we figure out what the letters should be we get:
With some careful anagram solving skills (an online solver) we can find the word:
Which would make sense as the answer because:
Explanatory 'showcase' answer provided by OP: All three of the existing answers here made great contributions to solving the puzzle (@Graylocke, @samm82, and @berkeleybross - to whom I have awarded the checkmark for being first to find the final answer), but none of them quite described the intended solution path in full (without making any assumptions), ...
I am updating my "full partial" answer to make it less rambling and confusing. The initial partial post was intended to start some other (cleverer) people solving the puzzle, but it looks like I am currently alone! :)
Firstly the part that we know is true:
From here we are working anew, with our given hints:
Fair point in ...
Solved! The answers to the quiz questions are as follows:
But - hang on a moment - there's something very familiar about the new barman, 'Tex'... What did he say to the Sergeant? "I'm four steps ahead of you"... There's something very susp- Wait! I know who he is!
How can we go about spotting this pattern? Well, first note that quizmaster 'Tex' ...
It is unfortunate that table markup doesn't work inside spoiler blocks.
Here are the answers to the quiz questions:
So we now have the following:
OK, let's work this thing out.
At this point we have
The state of play is now
What now? Well,
Now all that's left is mopping up. I won't insult your intelligence by showing ...
This answer was a group effort between @Graylocke, @berkeleybross, and myself, with a little confirmation from @Enigma, so I'm more than happy to make this a community wiki answer (unless there are any objections or @Stiv wants the +2 rep for accepting XD).
The answers to the questions:
What you should have done is
We can try the following
I have also noticed that
Hence, we have two valid and different solutions motivated by different aspects of the letters.