It took a while for the penny to drop for 13a. It's a classic!
Enjoyed this a lot and I find that having worked through the Azed back-catalogue doing 1 or 2 a day I'm getting better and seeing things like the shopping bag in 23a reappear.
One small ? Over the parsing of 16d. I assume the short somg is the second half of the answer (less 'one') but can't make anything fit.