The one that comes immediately to mind is Why did a young George Washington sign a document admitting to assassinating a French military officer?
the French commander offered Washington written articles of capitulation. He read them aloud to Van Braam so there would be no question what the blurred, water-blotched handwriting said. The preamble stated that the French intended "only to avenge" the death of Jumonville. Van Braam could not translate the next word. In the guttering candlelight of Washington's makeshift command post, it looked as if it were Passailir. Witnesses later had trouble remembering whether Van Braam translated it as "death" or "loss" or "killing." What the French later contended they had written had only one possible meaning: assassination. If Washington signed his name to such an admission, he was taking full responsibility, on behalf of Virginia and the English, for the murder of a French diplomat. Washington later said that what came next was what made him willing to sign: un de nos officiers. That was easy, "one of our officers."
Source: Willard Sterne Randall, George Washington: A Life (1997)
I'm quoting @LarsBosteen's excellent answer cited above.
Google also reveals some other examples
- BBC list of translation errors The Khrushchev quote, the 1830 negotiations both seem to be examples of simultaneous translations that affected history.
- Mental Floss provides a similar list with some overlaps; I'm not sure whether any of them fit your desire for simultaneous translation.
- Rosetta Stone lists another half dozen - the example of "intoxicated" is simultaneous translation, but I'm not sure whether $71 million dollars rises to the level of historically significant.
There are others - I just grabbed those from the top of the google list.