I draw the line when it's a TPC and a Sale price that are the same and obviously the TPC runs longer. I'll just toss the sale sign so there aren't two signs just hanging out.
Sorry, but even that won't fly. Even if the TPC runs three weeks and the Sale is only one week in the middle of it, you need to put up the Sale sign--because for that one week, the item is raincheck-eligible. If you throw away the Sale sign, nobody will know they can make a raincheck/substitute, and we lose potential sales.
The thing that gets me about the simultaneous Sale + TPC signs is that the ad prep team in my store will shoehorn both signs in the same spot on the shelf and make it look hideous.
Then you get all the whistle blowing yahoos on Consumerist calling Target a joke because "HEY LOOK! I'm calling out Target for putting up a sign when its not really on sale!". Seriously. Those stories run almost once a week.