I had a similar experience with the 2013 air (13"). It was difficult to adjust the viewing angle past 90 degrees, as the lid would fall back all the way once tilted past that point. I brought it to the store and they first attempted to tighten the hinges, but decided to replace the display instead which resolved the problem. This was done for free even though I didn't have Apple Care.
I read this thread, when experiencing the same problem with a 2 day old, MacBook Air 13".
Rather than guess, I took my machine to the Apple Store.
The kind of screen hinge problem listed in the initial question here is not normal. The 'Genius' replaced my 2 day old MacBook Air with a new one, which has a much better, stiffer screen hinge. I can now open the lid to any angle and move the MacBook Air around, without the lid moving.
If your MacBook Air is within warrenty, don't settle for a hardware defect. Get it replaced or repaired and enjoy your Mac again. We don't buy Apple hardware to have to compromise on quality.
I hope my experience helps someone.