The Mac App Store shows I have one update to install. When I open it, I am prompted to log in. When I do, it appears to accept my password, and then I get an error dialog that says:
"An unexpected error occurred while signing in.
The data couldn’t be read because it isn’t in the correct format."
Closing and reopening the Mac App Store didn’t change anything.
I just had that happen tonight also. I will bet there is a problem on Apple’s end. And I thought it was a weird error message as well.
Thanks, @raykloss!
I get a different error dialog on my MacPro running Mojave–but the same result. It will not accept my password and let me download an update. I’ve seen this happen before and it can take a few days to start working again.
I was just able to download the update without having to log in again. Go figure! 
Edit: And… it asked me to log in (giving the same error) just by switching into the Mac App Store.
This problem is getting coverage on MacInTouch and Michael Tsai’s blog.
Some folks are reporting that it is working again for them as of this morning…but I am still unable to access it from Mojave.
When I encounter things like this on older systems, my default assumption these days is an expired security certificate. I realize that may not always be a useful answer, especially if the mechanism for updating certificates is not always obvious or even available to end users.
It looks like this was a temporary server-side glitch.
I accessed the App Store yesterday on my 2011 Mac Book Air running macOS 10.12 (Sierra), and it seemed to work fine, both for downloading an update to an already-installed app and for getting a new free app. I was also able to access my purchase history (which required re-logging-in, since it had been a while).
I haven’t been able to access app updates for a couple of weeks, on systems running High Sierra. My user icon just isn’t there.
Indeed! Extended, but temporary. I confirm that I can now access it again.
Has not been working for me on Mojave, including today.
