The shop owner is likely to be within their legal rights to do this. As the property owner, the shop owner has a right to photograph anyone on their premises unless they are in a situation where they have a normal expectation of privacy (eg in a lavatory or changing room).
To comply with Data Protection law camera surveillance does requires a notice informing customers, so that is one thing to check (see the ICO code of practice for more information).
Minors generally have no special rights (but see elswhere in the FAQ for exceptions).
The most questionable issue is whether the owner has it on display for vindictive reasons or simply for staff guidance. If she has captioned it as "banned", or is telling customers the lad has committed some offence when he has not, then defamation may be occurring. However, proving this is likely to be difficult and taking any legal action likely to be far too costly to contemplate.
Law is not often much help in minor antagonistic situations like this. The best approach would be to try and resolve the problem by negotiation. If your son offended her, point out that he and you are embarassed by the photo, try and get him to say apologise in person for whatever he did (a good lesson in responsibility), then ask her to be generous. If after all that the owner doesn't respond favourably, then you have established they are being vindictive and it may be worth getting a solicitor to write to them.