granama1 - 18a in the def 'rag' = newspaper (anag 'Take the' + C[inderella]).
Chambers entry for 'log' gives 'fine'/punish as a synonym.
24 - take n[avy] from the usual 3 letters for 'smuggled',and the rest of your answer is a kind of rum.
A lot tougher than an Azed puzzle, I thought (but enjoyable) thanks for posting it.