Sense, in the end, that removing top cover could be a mistake (9)
I believe the answer is:
oversight
'a mistake' is the definition.
(I know that oversight is a type of mistake)
'sense in the end that removing top cover could be' is the wordplay.
'sense' becomes 'sigh' (I can't explain this - if you can you should give a lot more credence to this answer).
'in the' is an insertion indicator.
'end' indicates one should take the final letters.
'removing top' means to remove the first letter (I've seen 'removes top' mean this).
'could be' indicates an anagram.
The last letter of 'that' is 't'.
'cover' with its initial letter taken away is 'over'.
't'+'over'='tover'
'tover' with letters rearranged gives 'overt'.
'sigh' put within 'overt' is 'OVERSIGHT'.
Can you help me to learn more?
(Other definitions for oversight that I've seen before include "Failure to notice something" , "error" , "Supervisor's charged with this" , "Management" , "Carelessness" .)