The subject of Toph and her depth as a character has already been covered many times in this thread by her legion of admiring fans and I think you know that already. But for our drunk friend...
At the beginning it is difficult for Toph to connect emotionally with others; her encounter with Iroh is the first time we see her start to do this. That unlikely and instant friendship is what prompts her to return to the gang. We don't see her really open up to the others until season three when she has her fight and reconciliation with Katara; there we find out that she has mommy and daddy issues and isn't just a tomboyish wild child, she's actually very emotionally vulnerable. She's also insecure about her image, a problem stemming from her blindness, as we saw in Ba Sing Se. In the season finale she shows that she has the same fears as everyone else when she cries thinking that she and Sokka are about to die.
In short, calling her one dimensional is basically factually wrong. She has a clear character arc that takes her from being an emotional recluse, a product of her upbringing, to being able to connect with other people. What he perceives as one dimensional is simply the image she adopts because she doesn't know how to interact genuinely with people; the fact that it comes across as simplistic and forced is a testament to how well her character is written. And that's without even discussing the blindness: Toph is also a handicapped character but never shies away from her disability or allows it to define her--she lets neither man nor nature dictate her place in life.
I could go on, but I think that's enough to prove the point. If you still think she's one dimensional by the end of the show, you didn't pay attention to it. If The Legend of Korra can produce even one character with half the depth of Toph, then I will be ecstatic.
And I still wish I could hate him to death!