Well, you've got the potential of one dimensional, two dimensional, and three dimensional characters.* There's nothing wrong with a minor or walk-on character, who plays no real part in the plot, being one or two dimensional. You might want to avoid giving minor characters too much depth, because it distracts from the story.
Writers pick and choose which details to share with readers, they shape their writing, to guide the reader along. If the waitress who brings your main character a piece of pie while he waits for his girlfriend in the coffee shop is given several paragraphs of internal monologue in which we learn about her own messy love-life, then vanishes from the story, the reader may feel confused or resentful. However, if because of her messy love-life she chats with the MC and gives him some insights into his own situation, she's part of the plot, and that information is relevant. If she's just there to mention that he needs to order something or she'll have to ask him to leave (to underscore that his girlfriend is keeping him waiting) then the information isn't relevant - she can be one-dimensional.
Does that make sense?
There's also a distinction between minor characters and secondary characters. Secondary characters don't usually get as much time and attention as main characters, but memorable and interesting (ie. rounded) secondary characters can make the story considerably deeper and more interesting. They're the ones who are going to see the story through along with the main characters (and the reader), so you want them to be good company in some way or other.
Something to watch out for when working to round out your characters is the random addition of quirks or faults - you don't want them to become a laundry list of twitches.
If you decide to give a character a quick temper because he's too perfect, think it through and work out how that would have affected his life and other aspects of his life. How has he tried to deal with his temper? What sets him off? Are other people cautious around him, and is it harder for him to maintain friendships or be open with people because of that caution? Does he use the threat of blowing his top to get his own way? Or does he hate losing his temper because it makes him feel out of control?
There's some interesting discussion of rounding out characters in a number of the fanfiction websites, because of the fear of creating a Mary Sue (the utterly perfect self-insertion character).
-Barbara
*any more dimensions and you create a tessaract in the page and the reader falls through and is never seen again.