Also work retail.
Had a customer find a $20 scarf in a 50 cent clearance bin (where everything is clearly tagged). I explained that a customer probably left it there, because the entire display of scarves were hanging right next to the bins in clear view. Normally this would be enough for a customer to drop it. However, she kept arguing, and told me I "had to" honor the price. I told her we couldn't do that for every random item that was misplaced, because otherwise customers could just lie and say they found something in the wrong place (which they do anyway), and that we were clearly very busy and simply hadn't had a chance put that item away (our store is actually REALLY well kept). She put her finger in my face (this is what determined my behavior for the rest of my interactions with her) and asked me if I knew how to manage a store. Told her, "Yes, and as a manager I'm allowed to ask you to leave. So please do." Let me cashiers know that they weren't to sell her anything.
The next day she called the store and demanded to talk to a manager. I told her I was a manager and could help her. She didn't seem to recognize my voice and she recounted the story. Except, she lied, and said that she found a scarf in the clearance bin that was actually tagged clearance (which is something we would have honored). I called her out on this, and while she was yelling at me I hung up. Called my DM to explain the situation, just in case. But I never heard anymore about it.
The stupid thing is that had she just been a decent human being I would have given her a coupon (I believe it was 40% or 50% off that week) for her purchase. But I didn't have a chance to get my next sentence out before she started berating me.
My store is notorious for having somewhat confusing AD signs (I don't actually think they are, but people can't read), and 99% of the time we will honor them. If we forgot to take down an old sign, if the sign was placed in a confusing way, and pretty much any time the price discrepancy is within a couple of dollars, we authorize the cashiers to just go ahead and make the change. Pretty much the only time I stick to my guns is if a customer is being rude or there was no error on our part and the price difference is huge.