Hahaha I guess I'm bit late..yup, I'm sure they had tell you what you need. Some of the answers are right because you asks things that members often tease them for, but some are too sensitive that members didn't even mention it much.I guess amongst all, the obvious things that members like to tease is Donghae and his childishness/blurness..they like everywhere because of that..

Kyuhyun: members that they where against him joining SJ and that they had voted and more than 10 were against him.

Ryeowook: he is a bit sensitive about his looks and weight. When he was young he used to be a bit round.

-cont- dropped SJ for his acting career, etc

Ryeowook : short, make-up all the time, crybaby, bullying target, etc

Kyuhyun : game freak, a bit sensitive about the accident in 2007, stingy mouth, etc

Henry : dislike by some fans that prefer 13stars, etc.

I hope this can be useful shiv^^ hwaiting!:)

I'll just tell you the ones i know, because some of the other readers already said it.

Leeteuk : pretty sensitive about his plastic surgery, really like to flirt, a bit playboy, have a bad habbit sleeping anywhere, addicted to white, a bad temper if he was awoken by force, big mouth, dictator (according to hyuk),etc

Heechul : weird wardrobes, stingy mouth, fail aegyo, more beautiful than average girls, totally high temper, sometimes droll, mistaken as a girl, bad mood swings, etc

Hankyung : bad korean pronouncation, visa problem on 2006 that made him use mask for 3months, some fans that dislike him because of he's chinese (this one is a major prob).

Yesung : creepy, big head but small face, dark aura, weird habbit of touching other member's philtrums (esp siwon's), weird octopus dance, small hands, etc

Kangin : really like to drink, been involved in two accidents and got, been into jail because driving while drunk, high temper, really cheap to other members, big mouth, etc

Shindong : wheight, less attractive, almost no talent, Audition as a comedian but super junior as a career, etc

Sungmin : pink addict, likes to keep the probs to himself, really rare to cry, likes to be alone with his music instrument, etc

Hyuk : monkey, cassanova, playboy (not really), really like to borrow other's money (according to teuk), flirty, etc (i cant really tell his weakness because in my eyes he's perfect)

Siwon : dad problem, compared to other singer about how much is his money, gestures, horse, his facial expressions tells everything, too honest, etc

Zhoumi : about nationality being a chinese, not accepted by the fans that prefer 13stars, etc

Donghae : believed in supernatural stuff, been haunted by a ghost, really sensitive about his dad, childish act, fish-like face (no offense, he's handsome, the members said that), fail english (improved a bit), etc

Kibum : been told that he was really noisy and thats the reason he became really quiet, some people say that he -cont-

i'm almost the same with you...too obsessed with hyukjae
sorry for not helping :'(

Leeteuk - Can't play music with headphones b/c having phobia of getting attacked from the back. Maybe insecure of his injury from the car accident.
Heechul - Growing up, men/boys didn't see him as a man/boy.
Hangeng - Fans would curse at him and was treated differently under SM contract.
Yesung - Selca pic of his sweat appearing as a nose snot. Having a big head and small hands.
Kangin - 1st member to be enlisted in the army. DUI
Sungmin - Anemic & prediction of being a cheater.
Donghae - crybaby/sensitive, hates celebrating his b-day, hates being alone.
Siwon - father issue
Ryeowook - need to wear make-up 24/7 b/c of skin damage
Kibum - Fans berating him to be full-time singer and not part of SJ family.
Kyuhyun - During pre-debut, fans were unhappy he was added. Recovery from car accident & little hearing impaired.
Zhoumi - compared with Siwon.
Henry - "only 13" campaign

yesung is teased for his creepiness you no touching the philtrum, sungmin for his love shooting, siwon bcz his body, ryewook fr his make up #he always wear make up even just for meeting his parents, kyu for weird antic *drinking wine while listening to sukira and laughing out loud, shindong and kangin for their body, donghae for his childish act, heechul for being a scary diva... that's what i know though bcz i'm a jewel as well

kyu evil maknae forever, donghae 5 year old heenim diva sungmin spy i don't know the others kkkk and oh yeye touch people philtrum :-D

For Sungmin, he always got tease for doing the 'ending spy' move to his fans! He always 'shoot' his fan! Hahaha! End up SJ for months! Whenever they see sungmin they 'shoot' him. That was also the reason sungmin got the role in spy mv.

Am not sure about the other members though :( sorry! Not much of a help!

Heechul during their u promotions was attacked because he crack a note . Donghae has been tease because of his 5 year old mentality and his weird way of doing some dance steps . Sungmin the members said he is the manliest but I don't see it . Leeteuk laugh . Yesung and his weird habit if touching peoples philtrum

Well, I know Sungmin has this trouble about not being good in nothing in particularly. He can do anything but he can't do something that distinguishes him as the best in that area.
Donghae has issues with his father since he died. He's really sensitive and cries a lot.
Ryeowook also gets teased for being ugly and he hates skin ship.
Kangin with his past since he once was caught driving drunk and he was really careless so it brought a lot of trouble to sj.

I'm a little sleepy so I can't think straight, I'll try to remember more and let you know later...

wah i wanna help but me myself not so sure too.....for each member eh??