What ailment or flaw was Katherine Hepburn hiding about her neck
behind all the high collars and turtlenecks?

I wasn't able to find reference to any ailments or flaws. Perhaps, she
wore clothes like that just to cover some wrinkles?

Rainbow~

Once, someone wrote in "Parade" magazine that her neck was "crepey." 
But the height and extreme noticeability of all her collars starting
in probably her fifties was so consistent that it would appear
something more than wrinkles was being covered up.  In "On Golden
Pond" she has a swimming scene, and if you look closely, it looks like
a large varicose-style vein is there, but it was not easy to see
(obviously a lot of effort was made in her movies to keep her neck out
of the camera's view).  I was just wondering, now that she has passed
on, if there was information out there about why the extreme effort to
hide her neck.

Chattinoo and all --

I recall seeing an interview in which she said she didn't like the
prominence of her Adam's apple.  By Katharine's own accounts in "The
Making of The African Queen," she was very conscious of her looks and
had a mirror out frequently.

But in doing a little research there's also the fact that she found
her older brother hanging by his neck while she was still a teenager:
http://www-scf.usc.edu/~kristena/bio.html

Best regards,

Omnivorous-GA

Just my guess, but I thought the high collars and veils and all
appeared when the wobbles came on, and it was my speculation that they
were hiding a brace or device of some kind to keep her head steady.

Archae0pteryx