Sony forums are lit up too. They have a wide range of problems apparently.
Sony has so far acknowledged two problems that I can find.
1) a disc eject problem where the disc doesn't eject
http://community.us.playstation.com/t5/PlayStation-4-Support/INFO-Issues-with-ejecting-PS4-discs/m-p/42133811#U42133811
2) An improper seating of the hard drive problem
http://community.us.playstation.com/t5/PlayStation-4-Support/INFO-Proper-Seating-of-PS4-Hard-Drive/m-p/42138109#U42138109
The amazon part hasn't really been confirmed by anyone from what I can see. Some people are claiming its just amazon that has the problem though.