Add me to the "Broken Hinge Club". Late 2013 27" iMac purchased in Oct. 2013. Heard a loud "crack" in the middle of the night...loud enough to wake me even though the iMac is down a hall at the far-end of the house. Walked into my office the next morning and my iMac looked depressed, facing down, looking at my desk as if embarrassed . Tilted the display up and it just tilted back down.
I had purchased Apple Care before the year was up so I called them. They confirmed that they knew of this issue and that they were "looking into it". The gentleman said that they cannot do an on-site repair as the back panel has to be removed and they want it in a clean room, non-static area to prevent any other damage. Understandable I guess.
Since I use my iMac for business turning it loose for more than a day or more would be very difficult. So he called my local Apple Store and set up a Genius appointment. He said that they have a "lot of parts in stock" and should be able to turn it around quickly, but there have been occasions where additional parts were needed so they have to see it first. He also said that if they can't turn it around right away that I can have it back until any other parts arrive.
My biggest concern of course is that this will happen again. If Apple does come up with a stronger part I'd rather wait, but I guess there's no way of knowing if or when that might happen.
I've owned what seems like almost every Apple product made for the last 10 years or so and am über happy with them all. I've only had one out-of-pocket experience when a repair was needed (and that was for an older iMac graphcis card...the iMac was four years out of warranty so to be expected). Otherwise Apple has done a stellar job of taking care of any issues. Regrettable that someone let someone else approve this particular part. No one's perfect as they say. This iMac has been terrific otherwise.
I'll be taking it in this afternoon and will post back when everything's wrapped up.