Just about every single bug that was present on PC, is present in the PS4 release, including the weird text bug in the "Lover" tree (champion points).
The Harrowstorm at Hailstone bugged out something awful: it was stuck in a perpetual loop, red cyclone, lightning strikes that dealt damage, but no enemies, and no pikes. This caused my to be perpetually stuck in combat, and I could not logout under normal means, including the /logout command in the chat bar. I was all the way at the Solitude stables and still was "stuck in combat".
On the way to Solitude, runestone nodes and ore deposits were giving out just obscene amounts of resources. One rubedite deposit gave me 18 ore, and I went from having around 12 Kuta runes, to well over 50 of them, in just a 15 minute span.
Attempting to travel to the new Wayshrine in the new Reach area results in a guaranteed CTD for me, so I didn't even get to enjoy falling through the earth or having my screen freeze in a new dungeon. I will, however, give credit where it is due; lag/latency is essentially non-existent right now, even in highly populated areas (Solitude, Daggerfall, etc).
Yes, I have submitted tickets for these issues.