John Cleese's latest two characters complete special BBC radio show (5,4)
I believe the answer is:
loose ends
'complete special bbc radio show' is the definition.
I can't judge whether this definition defines the answer.
'john cleese's latest two characters' is the wordplay.
'two characters' can mean two replacements for 'character'.
'john' becomes 'loo' (both can mean a toilet).
'latest' indicates one should take the final letters.
'character' becomes 'e'.
'character' becomes 'ends' (I can't explain this - if you can you should give a lot more credence to this answer).
The final letter of 'cleeses' is 's'.
'loo'+'s'+'e'+'ends'='LOOSE ENDS'
Can you help me to learn more?
(Other definitions for loose ends that I've seen before include "Unfinished business" , "items to be settled" , "details yet to be explained" .)