We've seen a lot of reports, including Q&A questions, of sites showing bad dates in Google SERPs. I've verified this bug in the wild. There are also reports of bad dates being caused by YouTube embeds, with Google taking the video date instead of the page date. I can also confirm this is happening, although I don't know if it accounts for all of the bad dates.
Some people are reporting that these bad dates showing up corresponded with ranking drops. Usually, I would treat that as a coincidence (Google could easily launch an update and have a glitch on the same day), but in some of the reported cases, removing YouTube embeds led to ranking recovery soon after. I can't verify this, but I can't disregard it. There seem to be multiple reports of this recovery.
I'm in communication with a Google rep, and they are unaware of any direct connection between a bad date and ranking (such as some kind of QDF effect). I've passed along some data, and they are investigating, but there may have been multiple updates in play that are making for noisy data (even for Google).
There did seem to be heavy algorithm flux on November 10th and 18th, with some people speculating the latter spike was a reversal of the former. I have no evidence to support this, but MozCast data and chatter do seem to support both spikes.
If you've been affected by this problem and the ranking drops are severe, it's worth temporarily removing YouTube embeds (if feasible). Replace them with direct links (or maybe a linked thumbnail) and have Google re-fetch the page. I can't guarantee it will work, but the risks are low. It's easy to restore the embed.
Update (11/22) - Gary Illyes is saying on Twitter that the date problems have been fixed. If you see the proper dates cached, but have not seen rankings recover, then these may be unrelated events.