A recent update, 4.70, has been distributed to PS4 consoles today, and many users are reporting that the update refuses to download or screws with their PS4 altogether.
A 100+ post Reddit thread shows a long list of horror stories. Users are reporting the update getting stuck while downloading, the network connection failing, or the console refusing to get past certain screens.
Other users used the PlayStation community site to look for solutions to the problem, often coming with the error code SU-30625-6. This is not an all encompassing problem, as some users are reporting that they've had no problems whatsoever, sometimes adding that their PS4 is an original model. Some have been able to fix the problem with a few unpluggings and restarts, but others have said their problems persist.
At the time of writing, there has been no official word from Sony about the update causing issues.