I expect that any loading spinners on screen will eventually be replaced with content.
Specifically, I expect that the loading spinner below the Gravatar on the login epilogue screen will eventually be replaced with the user's display name and username. (Alternately, I'd expect to see no "Logged in as" section at all, if we can't load any user data.)
When a self-hosted user logs in, that loading spinner sometimes never goes away. I believe this happens when the self-hosted account is associated with an email address that isn't registered with a WordPress.com account.
Endless loading spinner:

Self-hosted account using an email address also registered at WordPress.com:

Hey @rachelmcr .
I ran across this when implementing the new login epilogue. Thanks for noting your thoughts on what _should_ happen because I wasn't sure. 馃槃
We might as well address this in the Unified Auth project, so I'm removing it from Groundskeeping.
cc @mindgraffiti
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Hey @rachelmcr .
I ran across this when implementing the new login epilogue. Thanks for noting your thoughts on what _should_ happen because I wasn't sure. 馃槃
We might as well address this in the Unified Auth project, so I'm removing it from Groundskeeping.
cc @mindgraffiti