Problem one: The funding for the creation and maintenance of these tests comes directly from the educational funding, reducing the amount that actually goes towards classroom instruction and programs that directly benefit students.
Problem two: The tests are created by for-profit groups with little oversight. This has led to catastrophic testing situations here in the state of Alaska and in other states in recent years.
Problem three: The tests themselves are not necessarily geared towards any state's curriculum, let alone any student's individual course load. For example, students who are taking calculus might find themselves answering questions requiring algebraic jargon which they had learned (and likely forgotten) four years ago. Despite knowing how to do high-level, complex mathematical computations, theses students' scores will often not demonstrate their true ability.
Problem four: The questions themselves are often trivia focused on unimportant minutia which is easier to use in multiple choice or matching questions but is not an effective measure of what students actually know. In fact, multiple of these tests have been shown to have outright errors in them.
Problem five: The test data is not returned to schools in any truly meaningful way. It gives hints as to which skills that might be missing, but not in a way that lets teachers or students truly know what needs to be improved.
Problem six: Parents can opt their students out of the test (in our district). In many cases, the students opted out are those who are on the upper end of the educational curve.
Problem seven: There's usually no real incentive for students to actually make a valid attempt on the test.
Problem eight: The testing environments are uncomfortable and the tests are overly long, encouraging students to rush through just to get done and out.
Problem nine: Often, the actual mechanics of taking the test are a hindrance to answering the questions. While many issues are now computer related, I remember one specific incidence where a student had accidentally skipped a line on a bubble sheet, putting their correct answers into the wrong spots.
Problem ten: The standards on which the tests are based are often vague and unclear, giving the tests too much wriggle-room to create "gotcha" questions.
There are certainly more issues, but ten seems like a good, arbitrary stopping point (kind of like the arbitrary stopping points on the tests).
I don't have solutions to all of the issues mentioned, but creating a worthwhile student reward system for taking the test seriously (perhaps demonstrated through test score and/or growth from previous tests) would be a good start.