Bias on standardized tests can sometimes be blatant.

This is an honest-to-goodness true story:

In high school, during the first gulf war, we took some standardized test or another. Can't remember which one. I don't think it was the Iowa Test; I think it was some new one. It had lots of different sections, including current events.

One question, I kid you not, was something to the effect of:

"Why are American troops fighting in Kuwait?"

Answers included:

"To protect US oil interests"
as well as
"To spread democracy"

I knew it was one of those two answers, but the "right" answer depended on who wrote the exam!

As for the broader question: I don't think there's any magic bullet solution. To test a variety of different types of knowledge and thought processes, one should apply a variety of tests. Teachers should be given the freedom to assess student learning and to hold students back who have not mastered the skills of a given grade level. Sometimes I think the one-room schoolhouse folks had it right -- grades should be tied to skill mastery, not age.