Note basic education contains nothing but fault (5)
I believe the answer is:
error
'fault' is the definition.
(I know that fault can be written as error)
'note basic education contains nothing' is the wordplay.
'note' becomes 'e' (musical note).
'basic education' becomes 'rrr' (the three R's - reading, writing and arithmetic).
'contains' indicates putting letters inside.
'nothing' becomes 'O' (looks like zero - 0).
'rrr' going around 'o' is 'rror'.
'e'+'rror'='ERROR'
'but' is the link.
(Other definitions for error that I've seen before include "Way of operating" , "1 down" , "A mistake or inaccuracy" , "Boo-boo" , "Miscalculation" .)