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: When Joshua is trying to guess the launch codes, it gets the characters one by one and "locks" them in. You can't "guess" a code like this. You have to get the whole thing correct at one time. Why would it take so long for Joshua to guess each character, if that's how things worked? If the code consists of letters and numbers then there's only 36 per character.