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Ung, quick note to unotheninja, having a poor upbringing isn’t really a negative character trait, and being blind is -not- a character flaw. It could conceivably be a mark of his flaws (if he’s literally drunken himself blind or something (can you do that?)). We are dealing with character flaws, which consist of behaviors or habits of behavior that the character could theoretically halt if they wished/checked in for counseling. 

Okay, on to the topic of over-seasoning the flaw pie. 
Interestingly enough, a lot of authors seem to love just flinging as many faults, traumas, bad childhoods, and everything else they can think of to beat on their character. We’ve all got a little corner of sadism in our hearts, I think, and some authors not only nurture it but turn it loose on their characters to maim and eat them. 
It’s not really such a bad thing. After all, conflicts are a big part of story-telling, and most people won’t read a story that doesn’t make them feel something. The thing is, sad things are kind of easy to produce emotion from. Character death, done wrong, is the crotch shot of the writing world. It’s cheap and once the reader learns to dodge it, you’re out of luck. 
Sorry, that’s getting slightly off-topic. Pulling it back to characters with negative traits in the possible surplus. My point was, it’s easy to heap on bad stuff. Sometimes, we get nervous- my character’s a real jerk, why is he like this? Did he have a bad childhood? When he was a kid, did his dog die? That’s not enough, he’s an orphan. His parents were murdered. In front of him. No, that’s been done 4,002 times. Um. After that he was put in foster care where his parents were abusive. He was finally adopted. Adopted parents beat him. Is that enough now? I want the audience to understand that he was just really unhappy—
       Stop.
Calm down and look at what you’re doing. You’re making a list. 

Your character could easily have a miserable childhood without one of those things happening to them. It’s about the details, it’s about the feelings. Clinically depressed people will tell you that their lives are fine. Their lives are great. They just can’t feel great. So calm down, and think of other ways than having a massacre. 
(Awkward moment when writing advice becomes talking down a murderer).
Also, with childhood- so many times, it smacks of Freudian psychology to me- they’re a jerk, what happened to them as a kid to make them this way? Plenty of jerks had fine childhoods, guys. 
Now. It’s also pretty fun, as authors, to make our characters total little bastards and then tell people what bastards they are.
The thing is, some people really appreciate a bastard. They like to whisper ‘bastard…’ in appreciation of what the character did that they would not (re. the entire premise of House). So it’s totally possible that yes, you can write a sympathetic character with lots of bad traits. 

What I’m trying to say, (forgive my lengthy in-eloquence), is that, rather than going for quantity, go for quality with your traumas and your bad traits. If it’s not working, don’t heap on more, rework what you’ve got to make it better first. It’s not a pile-on race. 

Hope something in there was useful,
-Evvy