Basically, I think Wittgenstein was too quick to pattern-match every mention of such things as "national character" with propagandistic nationalist ramblings.

You suspect he's too quick to pattern-match every mention from a single example?

I suspect this is just an instance of a bias that's been widespread in the Western world for quite a while now, namely the tendency to write off the use of certain kinds of conditional probabilities about people, including most of those conditioned on national origin, as inherently incorrect or immoral.

I'm aware this is a common bias now, but I don't think it was that widespread in 1939.

Moreover, from the "wouldn't surprise him at all" comment, it does appear that Wittgenstein had, for whatever reason, a biased unfavorable view of the British government.

Perhaps this is because I have an unfavorable view of governments in general, but it seems that for an even slightly cynical student of history assassination attempts on rival heads of state by a government should not come as a surprise, especially as monarchies were replaced by democracies. It's not clear he was singling out the British, and even if he were singling out the British, it's not clear if that was the result of bias or cool calculation. (The British did have the best spy network in Europe, although whether or not Wittgenstein would have known that is not something I am able to guess.)

I agree that being biased can lead to fury, but I think for someone as passionately logical as Wittgenstein seeing bias, especially in a friend, could also lead to fury. It's not clear to me that his immediate reaction is evidence between those hypotheses, and his persisting fury strikes me as slightly better evidence for the latter. (Background: Almost twenty years earlier, Wittgenstein was rebuked as a teacher because he would also beat the girls if they made mathematical mistakes.)

That is, it is possible that Wittgenstein was biased in pronouncing Malcolm's bias, but it seems to me unlikely. The evidence seems to point the other way, especially the conclusion he draws- that philosophy should help one with the important questions of everyday life.