Should I correct grammatically incorrect quotes when using them in a paper?
On both the original EL&amp;U post and this one, people have asked &quot;why do you believe that you cannot you use &quot;[sic]&quot; in a formal paper? On the EL&amp;U post, you wrote:

I don't [sic] about other areas, but in science/technology where I work on [sic], [sic] would be considered a cheap way to discredit others. It is acceptable/understandable there will [sic] be editorial mistakes (the paper is about some other topic, and it is fine so long [sic] it makes unambiguous sense). In certain cases, [sic] where we see [sic] the result is indeed wrong, we say it politically correctly (e.g., we are not able to reproduce the same result [quotes missing in original]). In all likelihood, pointing out editorial mistake would be taken badly by the community.

So the perceived issue is not really about formality, but about offending the original authors. And indeed, quotes with many mistakes will require many instances of [sic] (as above), which hinders readabilty and, I agree, seems rather passive-aggressive.
On the other hand, you absolutely must not &quot;fix&quot; quotes. Even benign changes can cause problems; for example, think about how many well-meaning editors might change &quot;iff&quot; to &quot;if&quot; in a math paper. It is probably acceptable to insert missing words in brackets [like this], but that's probably as far as you can go.
So, to your question, I would suggest the following:

If there is a single mistake you could either use [sic] or (in the case of a missing word) insert the missing word in brackets. No reasonable author should be offended by this.
If there are many mistakes, you should probably not quote it at all. Instead, summarize it in your own words. As a last resort, if you absolutely cannot avoid quoting a lengthy, error-ridden passage, you could say something like &quot;[spelling and grammar errors in original]&quot;; this would at least reduce the awkwardness to a single sidebar rather than peppering the quote with [sic]s as I did above.