Dispensed diagnoses overlooking nothing unusual (8)
I believe the answer is:
assigned
'dispensed' is the definition.
(assigning is a kind of dispensing)
'diagnoses overlooking nothing unusual' is the wordplay.
'overlooking' indicates named letters should be taken away.
'nothing' becomes 'O' (O resembles 0).
'unusual' indicates an anagram.
'diagnoses' with 'o' removed is 'diagnses'.
'diagnses' is an anagram of 'ASSIGNED'.
(Other definitions for assigned that I've seen before include "selected" , "Allocated" , "Appointed to a duty or task" , "Allotted or appointed to a post" , "Given a task" .)