What is the ruling on working in a halal meat shop if it becomes apparent that some of the meat displayed may not be halal, given that the owner is aware of this and unconcerned about the matter?

If the shop is designated for selling halal meat, and its owner is trustworthy, and the country is predominantly inhabited by People of the Book, then the default assumption is that the meat is halal. Consequently, there is no harm in working there unless it is definitively proven, or highly probable, that carrion is being sold. Mere doubt, however, should not be entertained.

If it is certain or highly probable that the shop sells carrion and its owner is aware of this and persists in it, then it is not permissible to work there, as it constitutes cooperation in sin. Carrion is strictly forbidden by explicit Quranic text: "Forbidden to you are carrion, and blood, and the flesh of swine" (Al-Ma'idah: 3). In this situation, one must leave the job and seek a halal alternative.