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Obviously, this only applies to subtitles from English speaking works, since I can't exactly vouch for the accuracy or lack thereof of any others.
The most recent example of this I can think of is from Dark Souls (or more precisely, the additional content) where, if you kill Ciaran, the subtitles leave out the last line of her death quote ("My... dear... Artor..."), which, from a story standpoint, is a pretty important line. Another example I can think of are the subtitles for Portal, which flat out lie at points. Whilst I mostly use subtitles so I can make certain I've heard everything that's being said correctly, for people who actually need them, this can range from mildly annoying, to massively problematic. Granted, it makes sense if the subtitles are being done on the fly, but for the most part, that isn't the case.
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The subtitles for Portal flat-out lie at points, but then, so does GLaDOS, or are you referring to lying in a different sense
The subs say stuff that GLaDOS isn't saying.
What he said.