White coats in cats are definitely linked to deafness. It's pretty common. Other stuff, I'm not sure. I want to say eye problems too, but I might be thinking of dogs (a lot of white dogs have eye/ear issues).
ETA: Some stats about white cats and deafness (the eye thing I was thinking of is about the blue eye link) From: http://www.messybeast.com/whitecat.htm
-95% of the general cat population is non-white cats (i.e. not pure white) and congenital deafness is extremely rare in non-white cats.
-5% of the general cat population is white cats (i.e. pure white). 15-40% of these pure white cats have one or two blue-eyes.
-Of those white cats with one or two blue eyes, 60-80% are deaf; 20-40% have normal hearing; 30-40% had one blue eye and were deaf while 60-70% had one blue eye and normal hearing.
-Of the 5% of white cats in the overall population, 60-80% had eyes of other colors (e.g. orange, green). Of those 10- 20% were deaf and 80-90% had normal hearing.
-Deaf white cats with one or two blue eyes account for 0.25 - 1.5 of total cat population
-Total number of cats with white coat and blue eyes account for 0.75 - 2.0% of total cat population
It is evident from those studies that blue eyed whites exhibit a higher incidence of deafness than do orange/green eyed whites or non-white cats! But not all blue eyed whites are deaf and here's why:-
There is a known link between white coat color, blue eyes and deafness - but since the coat and eye color can be caused by different genes it means that only some blue eyed whites are deaf. There is a gene/gene complex which causes white coat, blue eyes and deafness, but not all cats get their white coat and blue eyes from that particular gene, so not all white cats will be deaf.
Solomon - black DSH - king of kitchen raids (11)
Gracie - Mutterooski X - scary smart (9)
Jaida - GSD - tripod trainwreck and gentle soul (4)
Heidi - mugsly Boston Terrier X - she is in BIG trouble!!! (3)
Audrey - torbie - sweet as pie (11 months)
Patrick - blue - a little turd (but we like him anyways) (6 months)
Boo, our Matriarch (August 1 1992 - March 29 2011)