In E&W (not sure about Scotland) the current Defra guidance states
It is permissible to source certain types of former foodstuffs (see above), as well as fruit and
vegetables, from non-catering premises for feeding to pigs, but this must only be done from
those premises that either do not handle materials banned from being fed to pigs, or that have
(HACCP) procedures in place to ensure complete separation from prohibited materials, and
these procedures have been agreed with the local authority.
Most supermarkets have haccp procedures in place, and certainly if you were a veggie buying a bag of apples you'd be pretty disappointed to find that Tesco had been rubbed them against a steak before being packed ! So buying food is generally thought to be different - although as above technixcally the store does need to have told they LA.
If you taking waste from shops you'd need to check that they have handling procedures in place to keep waste seperate (and that these have been agreed) - as shops are not allowed to let waste meat go to landfill, you'll find that all supermarekets or multiples have procedures in place, and even single shops should have haccp in place.
Generally whilst if you're sensible there is no risk, it is better to just talk to your local AH office and get their view, and if you do, let us know on this forum what they say. Suspect a no will be the easy answer for them.