Off duty police who are hired for security have the same authority as when they are on their scheduled tour.
That is one of the main reasons they are hired instead of some $8.00 an hour Rent-A-Cop.
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.