If a trader places an MOC order that should have been hit, does the Specialist ever not fill the order or fill it at a price that is worse than the opening print?
MOC is a market order, so as long as it's in on time you are guaranteed a fill. Has to be submitted no more than 20 minutes before the close. The price you get will have nothing to do with where the stock opened.
Yes, if you are offsetting a published imbalance, you can submit after 3:40. Updated imbalances are published again at 3:50