Something to swat with The Observer? (3,2,3,4)

I believe the answer is:

fly on the wall

'observer?' is the definition.
(a fly on the wall secretly observes things)

I don't understand the rest of the clue.

(Other definitions for fly on the wall that I've seen before include "Bug in room" , "Unseen observer" , "Unnoticed observer" , "inconspicuous observer?" , "Unobtrusive documentary" .)

I've seen this clue in The Times.

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