That seems to be a rather tenuous line between public good and abuse of power. While I agree that a police officer should be able to enforce the law while off-duty, I do not agree that private sector entities should be the beneficiary.
Not to belabor the point but we the people lend certain of our rights to government. One of those is the right not be be imprisoned. By allowing government to hold this right we have a better society. That being said, Walmart, Sears, etc are NOT government and as far as I can tell have never been granted a damn thing by the citizens of this country. So why then should their employees have police power, regardless of what that employee does for a living.
They will also let you know that the same officers patrolling your area while on duty are available to provide additional coverage after hours if you are willing to pay for the service.
It is a way of providing police coverage without adding personnel or increasing the budget. If you want more than the standard coverage you have to pay for it.
I'm not saying it's right or wrong, I'm just saying that's the way the system works. So people who pay the extra for real police protection or security expect the officer to have the authority to actually enforce the law.
I know a Sheriff’s Dept. deputy who makes more on his after hours work than he does on his scheduled tours.