Apparently, it is indeed legal and there's not conflict of interest for the police officer. He is an officer and a security guard. He doesn't get paid extra for making arrests, but Dillard's used to prosecute EVERY case of shoplifting--no matter a 5 dollar item or 500. A lot of the officers, however, didn't to bother arresting someone for stealing a single lipstick. They would hand out warnings or take the item back and just "escort" them from the store, which made store's head honcho a bit peeved.
There were also many news-worthy cases where the police went a bit overboard and beat a shoplifter so badly, the man died, and a few cases of an in-store fight with thieves resulting in shots being fired. Dillard's was always being sued or investigated for something---harassment, discrimination, police abuse, etc.
I worked there for years. Not a fun place to be employed, not by a long shot, but the off-duty officers were all great guys and I never had any problems with them. In fact, they would escort me to safe every night when I made the daily deposits.