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If my manager says something that I know to be factually incorrect, how can I
point that out without sounding disrespectful? (Is ~違います appropriate in this
context or is that too strong?)

Is this a situation where I would use speech that is more formal than usual?
For example, would I switch to a form of keigo for this even if I normally
have a more informal relationship?
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politeness culture business-japanese
How would I respectfully disagree with a superior?
Dave hit it right on the spot. You don't disagree. You have to agree and then
offer up your own idea as addendum while stating that you are unsure. one way
to disagree is "その考え方もあるけど．．．"
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2011-06-15T03:04:51.717
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Not a _bona fide_ answer, in that I am not confident enough to provide you
with a reliable example of what you should be saying, but I can definitely
tell you how you should **not** be saying it (despite some suggestions in the
comments to your question):

  * Any sentence that **starts** by a word expressing disagreement.
  * Anything that hints at an actual error made by your boss: "間違っている", "間違い" or, Amaterasu forbid: "違う！" etc.

In fact, the two points above are probably good guidelines for _any_
argumentative discussion with a Japanese person. I know the whole [resolution
by consensus](http://en.wikipedia.org/wiki/Consensus_decision-making) thing is
a bit of a tired cliché about Japanese society, but there is a reason it
became one: you can safely expect Japanese in general, your business
associates in particular, and your boss _most definitely_ , to dislike direct
confrontation even (particularly) when they are factually wrong.

The standard recommended way to handle both a personal or a business
disagreement (there is no such thing as a factual error in Japanese, only
differing viewpoints ;-) is:

  * Start by agreeing wholeheartedly (そうですね etc).
  * Introduce your correction/viewpoint, as if it was some last minute detail you just thought of, that was of no importance whatsoever, or as an _improvement_ , rather than a correction.

Of course, I am drawing very broad strokes here and standard use-your-better-
judgement disclaimer applies, but I think you can't really go wrong with this
approach.
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2011-06-15T03:51:34.077
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I use something like

> それもそうですけど、。。。。
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2011-06-15T03:55:17.783
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You could say something like "難しい…" and let time pass by a bit. It expresses
your difficulty with accepting what has been said, letting everyone enough
time to reconsider what has been said.

You could ask for confirmation: "そうですか". It will ask for more informations,
possibly allowing the fact to be shown wrong.

P!
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