Plot hole: Given the number of possible combinations the launch code could be (over 3600 trillion possibilities) it makes no sense that W.O.P.R cannot process that significantly quicker given how easily it's able to calculate thousands of ICBM impacts, damage inflicted, casualties, etc. for each "War Scenario" at the end as quickly as it does to determine a winner.
Plot hole: At the end, the suggestion to unplug W.O.P.R. to prevent the missiles from being launched was actually the right suggestion. Given that W.O.P.R. was guessing the launch code by brute force, the actual order to launch the missiles wouldn't be given until the launch code was determined and therefore the silos would not interpret anything until they received not only the order to launch but with the right launch code.