I assume that ten problems of any category are posted at a time. While this works, some categories move slower than others. Here is my proposition (although I don't know squat about programming, so it might not be able to work).

THE CANDY MACHINE SYSTEM

  At any given time, one problem from each category is up for review. In a candy machine, you don't just buy whichever ten types of candy are in the front . . . you can pick any one of each type of candy, and none are duplicated. "Liars and Knights" and "Weights and Scales" might have seperate sections from "Logic Problems", or they might all be together. This way all the problem queues would move at relatively the same speed.
  Once a problem is pushed through to floobledom, a new problem of its category will fill its slot. Only a certain number of problems for each category would be available at a time. (Candy machines do not have infinite supplies.) Once a problem type is exhausted, you have to wait until the next day when all the types are "refilled" and ready for viewing. This way, no certain category would move too fast or too slow.

  Again, this system is just theoretical. I have absolutely no clue how it would or could work. Just a suggestion.

  Yeah . . . if it even can work at all. Remember, I can't program squat.

  What if . . . only a certain number of problems were in the candy machine at a time? Then five or so Algorithms or Calculus puzzles could be reviewed until the machine ran out. It could be replenished daily.
  But this might add another hour of programming. I wouldn't know.

"While this works, some categories move slower than others."

Why do you think this is the case? Certainly there are fewer problems in some categories than in others, but yes, we see 10 problems of all types, and they are reviewed, voted upon, and pushed in about the same order as they enter the queue, which is in turn the order in which they were submitted. If one of every fifty problems is a calculus puzzle, then one of every fifty problems we look at is a calculus problem.

The FIFO system is not only the simplest, but in my opinion, a better model than some complex category-based method of selecting problems for review, not to mention fairer to the people submitting problems. The changes would not only be messy to implement, but as Brian noted, would mess up the order in which problems move forward.