We've been getting many PS4's coming in with broken HDMI ports and I highly doubt its an "isolated incident" as mentioned by Mr.Yoshida (Sony President).
I mean what else are they going to say? "Yes, we're sorry, but we used cheap parts on these HDMI components and didn't do enough testing." It would be silly for them to admit to this problem with the 1st generation Playstation 4's. Best approach would be to ignore it as much as possible and it will go away by itself.
If you just want it get it fixed, go here: PS4 HDMI Repair + $50 rebate