I have some Level III (message level) data for equities and I have found several cases in which I register the execution of a Limit Order at a price "worse" than the best bid or ask.
For example, let's say that the Best Bid on that exchange is
$20.48 and that there is considerable depth at that price (say, 20,000 shares.) I have several cases in which I have a "full execution" message for a Buy Limit Order (on that same exchange) at price
$20.47 without anything happening to all the Buy orders at $20.48... How is that even possible?