You've plotted and drafted a mystery. Good on you. Now it's time to get out your scalpel and slice it to shreds. (Can you tell I love revising?) Of course, many of the concerns you'll have are the same for stories of all genres:
*Do your characters track? Are they behaving and thinking consistently throughout the narrative? If there are inconsistent moments, are they motivated enough to they make sense to the reader? Often in mysteries characters are revealed to be someone very different than we thought they were, but any big personality shifts should be explained.
*Have you answered any and all questions raised? This applies not just to the big whos and whats your protagonist is after, but also smaller issues, such as an obstacle they meet along the way. Are there any dangling threads that need to be sewn up? If they lost a purse in an early chapter, we need to know how they are carrying their money, and where the purse went.
*On the other hand, have you created enough obstacles for your protagonist? If anything seems too easy to you, it will definitely feel like a cheat to the reader. Believe me, I have tried many times to get around the break-in scene and my lazy nature means there's always some convenient key or code (ta-da!) in the early drafts. Eventually (and sometimes with editor prodding) I have to throw those away and do things the hard way.
*Is every scene — every interaction— moving the story forward? Is conflict always in the foreground? Again, true of all stories but in a mystery that question of what the heck happened to so-and-so should be on the reader's mind on every page.
But here are a few other things to think about to especially strengthen that mysterious mystery element:
*Is the dialogue as tight as it can be? Are your characters spelling out too much or talking too literally in conversation? (Often we write as we think things through in our heads... but the reader doesn't need all of this info, and in fact the story will move along more deftly without it.) Can they say the same thing in a more subtle or elliptical manner?
*Have you left enough clues along the way so the reader can piece it together? (But not too many, of course!) Walk back from the ending and make sure there's a legible trail. Remember that your reader is smart, and will put it all together, but not if you make the murderer an alien that swoops down in the third act with no prior warning.
*Are any aspects of the story TOO predictable? How can you play with readers' expectations? If the reason your thief skipped town seems obvious to you while you're writing, it's probably not a good basis for a mystery. Push yourself on the next draft to acknowledge easy plot points and by all means, use them as red herrings, but come up with a different solution.