One time the game crashed on me when I was fighting a giant mech/tank thing with a couple of other people, but it didn't crash to the menu or anything, it straight-up glitched and went all yellow and purple. It was weird! I had to reboot my PS4. Other than that I never had any problems.
I have both an Xbox One and PlayStation 4 and I like the Dualshock 4 a little more. I think the sticks feel better and the D-Pad is really nice. The Xbone controller is nothing to sneeze at, though, I just hate the new bumpers. They feel super awkward and they're very difficult to hold in (like when I used the binoculars in Black Flag). The only problem with the DS4 is that the battery life is absolutely dreadful. I can play for about 4 hours before it needs charging, though I have dimmed the light bar since the update. Maybe it lasts longer now, I dunno.
As an early adopter of the PS4 and XONE, I'm still waiting for that ONE game that makes me happy about my purchase, but I am excited for the crop of 2015 games. This year is looking a little thin for me personally, but Destiny looks pretty awesome.