In short, don't notice nobleman might calculate it incorrectly (8)
I believe the answer is:
miscount
'calculate it incorrectly' is the definition.
I can't tell whether this defines the answer.
'in short don't notice nobleman' is the wordplay.
'in short don't notice' becomes 'mis' (I can't explain this - if you can you should give a lot more credence to this answer).
'nobleman' becomes 'count' (count is a type of aristocrat).
'mis'+'count'='MISCOUNT'
'might' acts as a link.
Can you help me to learn more?
(Other definitions for miscount that I've seen before include "Make error with 20 [ABACUS]" , "total boob" .)