Too flawed would be a problem if you couldn't manage it. I'd think we like flawed characters because we want to see them "fixed" (Not like pomerainians, mind you). We want to see them over the course of the book fix or at least try to fix their flaws. ADD: Also, since as humans we're inherently flawed, we want to compare our skeletons to what the author comes up with to see if we rate a "phew, not me" or "wow, mine suck worse."
Another axiom is that people with "flaws" are "dangerous." So, we like to hang around dangerous people because we're too scared to do these things ourselves. Living vicariously through them. So, that makes sense. We live through the characters in the book, and I'm sure I'm not the first person to say that.
That said, alluding to a flaw means you need to substantiate and explore it at some point. The more flaws, the more substantiation. All the flaws are tied together in the human machine, so, you'd have to interconnect them. So, it becomes a management issue: how do you manage all these things within your character and still carry off your plot?
I'd recommend if you're just starting to keep the flaw count low.
Then, as you gain grasp and control of working through the processes, add more in future characters.