cocanuts reports the logged-in-as-another-user bug
itsaserket reports the logged-in-as-another-user bug
rachelmanija reports the same bug (and also reports that it stopped happening to her) (ETA: she expanded on what the bug looked like in comments here)
nix_this reports the same bug (with other details in nix_this's lj)
kazzisato reports the same bug
... but there are a ton of comments on the lj releases post now; those are just the first reports of the problem that I saw. LJ staff have not yet commented to my knowledge, so all that there is so far is a series of bug reports - nobody seems to know the extent or scale of the problem, whether it was a temporary glitch that has already been fixed or whether it's ongoing, or basically any other details. I haven't seen any bug reports from users who noticed unauthorized access of their journals - just from people who noticed being logged in as someone else.
There's also an overview post about this lj bug at unfunnybusiness. There don't seem to be any suggestions for fixes yet, but the lj release entry for their recent code release has 800+ comments and is growing, and I haven't looked at everything. I haven't seen any reports on why it's happening, but some folks are suggesting that it might be related to an (unannounced) change in handling cookies that has also affected plugins like LJ Login and dreamwidth's comment importing.
Unfortunately, while you can tell pretty easily if you have access to the wrong journal (click edit entries, see what happens, if something goes wrong log out and log back in), so far there's no way to tell if anyone else has access to yours. Will ETA if I learn more.
ETA2: fallacy_angel took a screencap of the journal they were temporarily logged into; see also their comment at lj releases.
ETA3: Strike ETA1; I think dapperdinosaur is reporting the bug shortly after it happened to them, which makes a bug report from about 4:00 am UTC on the 27th.
ETA4: lorax experienced the bug at about 3:15 pm UTC on the 26th, and wrote up an detailed report of what the bug looked like plus some notes about lj's response.
ETA5: In the comments here, silveraspen describes the response to their pm to a site staffer (at 2:46 pm UTC on the 27th) which suggested that info was going to go up at lj_maintenance soonish.
ETA6: There's a new lj maintenance post that describes the problem: they're saying that it didn't allow people to edit other users' pages, just view them, so it wasn't a security risk. (This is one of the times when I facepalm about lj's communication - site security vs security of people's info would maybe have been a good thing to mention there.) They also describe it as a bug that lasted for only three minutes - while it's true that most of the bug reports I saw were clustered around the same time period, I've also seen a couple more recent reports, so that seems ... unlikely.
ETA7: Make that a really recent one - here's snailbones's report of the problem happening after that lj maintenance post was made.
ETA8: This is the first instance I've seen of someone saying that they actually did something with the account they were logged into (I think - it's somewhat confusingly worded, so definitely grain of salt here), plus some discussion of how long the problem was happening: misstiajournal's comment at the lj maintenance post.
ETA9: moropus also reports that they accidentally commented as another user when they experienced the bug (note that the comment also has anti-Russian sentiment)
ETA10: siljamus talks about things to do to minimize the risk of this happening to your journal, which mostly involve logging out of all of your livejournal login sessions, and then not logging back in at all (which includes not crossposting from dw).
ETA12: LJ mentioned the problem in passing in their most recent lj news update; many of the comments are angry about the in-passing remark, wording, challenge the details, etc.
ETA13: rachelmanija describes what the bug looked like (what she could see, how long it lasted).
ETA14: strike ETA11; majoline reports seeing the bug (or a different bug?) at about 3:30 pm UTC on 10/29. This bug report is different, though - they were taken to the edit entries page of a journal entry they clicked on, not to a random journal.
ETA15: It turns out that anyone can see anyone else's edit-entry page for a public post by putting in their username and the number of the entry; it only works for public posts, and it grays out the boxes and nothing can be clicked on. So a misdirected link could send someone there, and so could I if I manually entered it, and etc. darkspirited1 and xenotaku have been figuring out the parameters of how this works in a comment thread. The existence of this weird UI is irritating, because it means that the cache error(?) bug and this thing might be described in the same way by a user. The important differences seem to be that in the cache error, someone appeared to be logged in as someone else, so the edit entry page would appear normally but with someone else's data (buttons appeared pushable, someone else's username and icon, etc), whereas in this edit entry page looks weird and unusuable (buttons and text greyed out, at the top it looks like you're trying to edit a post in a community: [yourusername] in community [otherjournalname]).
ETA16 I just saw another new bug report on lj maintenance of something weird that looks a bit like the original bug circa 4:53 pm UTC 10/29. Their comment with screencaps got marked suspicious, but since the comment was emailed to me I saw the screencap, and they said I could link it here: screencap of the post entries page as snowsoftsong. It looks like the post entries page as if someone else was viewing it - there was no "in community..." or anything and the entry page wasn't greyed out - except that the username was snowsoftsong, and the original poster of that post was alwaystheheart in a different comm. So: WEIRD.
(Almost) everything I've linked to in this post is a single user's bug report or description of their issues - I have no way of checking the veracity of anyone's comments.