I have issues, you have issues, everyone has issues. As writers, even our characters. Especially our characters, hopefully.
I belong to a weekly critique group led by the amazingly talented YA author, Bonnie Hearn Hill. She says that everyone has a hole in their heart that really lends to who they are, and what motivates their actions. She always wants to know what our character's "hole" is. This has been so helpful in my writing and in creating authentic backstories for my characters.
Why is it so important for your characters to have issues? Well, I think most importantly, because it makes them empathetic. It's hard to like someone who's perfect, or read about them, because for one they're not interesting, and secondly, because we can't relate. We read because we want to see ourselves on the paper, and we want to see the characters making the same kinds of mistakes, having the same kinds of problems that we do. It's human.
It's kind of like how some women tend to always go for the bad boy. Why do they do it? Because they see vulnerability within them. Take Captain Kirk in the most recent Star Trek movie. He was definintely a bad boy, but he was an empathetic character becaus we knew that the reason he was having such a hard time was because his dad died when he was young, his mom was always away on other planets, yada yada yada....and we liked him despite his actions because we believed he was really good on the inside. He has issues, and once we saw that, we started to root for him (well, and Chris Pine is sort of gorgeous...)
So anyway, if you have a character who is seemingly perfect, you better rethink that. Give them some character flaws, create some backstory, and you'll go from making your characters from flat to round.