Thus was it written: quoting accuracy and pretentiousness
When you see [sic] in a quote, it is short for sic erat scriptum, which means “thus was it written” — a rare case of an English translation that sounds even snobbier than the Latin. It is used to highlight that an error in a quote was found in the original text. For example:
“Learn from the misteaks [sic] of others. You can’t live long enough to make them all yourself.”
Eleanor Roosevelt
Accuracy in quotes is not all it’s cracked up to be. In many cases, if not most, you should really just fix that error, instead of playing with Latin abbreviations.
You can also simplify and paraphrase as needed, within reasonable limits. Really, it’s going to be okay. Nothing terrible is going to happen.

The offending quote: “The cat sat on the mat.”
The original: “The dog lounged on the chaise lounge, but the cat sat on the mat.”
To the uptight pedant, the quote should begin with “…the cat” or “[T]he cat,” using the conventions of scholarly quoting to explictly denote the slightest deviation from the original.
Ridiculous! That’s just typographically awkward, with no benefit other than the satisfaction of slavishly following the rules. It’s like insisting that every cropped photo has to have a dotted-line and scissors indicating where pixels were excluded. It just calls attention to itself and burdens your quoting with pretentious subtext: “I’m deliberately making you wonder what was omitted just so I can show you how diligently I quote stuff.” Using sic when the error is trivial and innocuous is downright passive-aggressive, towards both the reader and the person quoted — just repair the silly thing.
There are times when precision matters, of course. If you’re quoting a commander-in-chief while a nation hovers on the brink of war, you do need to get that just right (and erring on the side of including any relevant context, too, rather than cropping it out).
But most quotes simply don’t matter that much, and clarity and simplicity should take precedence. I have no editorial/ethical issue with making minor corrections to quotes as long as they still clearly communicate what their sources obviously intended.
The only reason I would not correct a clear mistake is if it was somehow relevant. For instance, if I am quoting a chiropractor who has spelled “interverbal joint” instead of “intervertebral joint,” I am definitely going to sic a sic on that amusingly ironic error. That’s one of the best possible of example of errors that are actually a feature of the quote. If you have one of those, sic at will
But we can and should be less uptight about quoting, and there’s even a place for paraphrasing. On Twitter, for instance, I have taken to “gentle paraphrasing,” actually editing a quote to fit the limited space, because it just isn’t going to happen without an edit. I think as long as the spirit of the statement is preserved, it’s just fine. Certainly no one has complained yet (especially because for the most part the tweet links to the original).
Finally, it’s worth noting that many quotes simply do not have a canonical version… or not a good one. There are numerous famous examples of quotes that were relatively laborious or sprawling in their original form, and then a simplified version eclipsed it. Trivial simplification for clarity may feel weird with a fresh quote, but there is plenty of precedent!