Expedite iOS app review to less than 24 hours

I have heard of people using their paid tech support instances to expedite a review or determine why exactly it's being rejected if there is a code problem (such as Apple suspecting that a private API is being called when you are not calling any private API), but your best bet is probably to follow the normal process outlined here:

• https://developer.apple.com/app-store/review/

Urgent Bug Fix If you've submitted an update to fix a critical bug in your app on the App Store and you are requesting an expedited review, be sure to include the steps to reproduce the bug on the current version of your app.

Be sure to explain why the bug is critical before you burn a chance at an expedited review. I would call someone that's not a software developer and have them give you an honest reaction if your bug is really critical after you take 60 seconds to explain to them the nature of the problem.

If you can't explain to a lay person in 60 seconds why this is critical to them as a potential user of your app, you might not get Apple to bump you to the front of the line. If your description of the critical nature of the patch is in the end user's interests, this seems to be your best shot to move things to the front of the queue.

The expedited app review process still takes time, I have seen app developers wait from a few hours to a few days and in really bad cases, weeks. I have also seen app developers try every possible way to speed up the process (finding the review team on Facebook, Linkdin, etc..)
In regards to your specific problem, that's the reason we created rollout.io an SDK which allows you to solve quality issues in production instantly, the solution is fully complient with Apple's guidelines.

Disclosure: I'm one of the co-founders of Rollout.io

P.S This site shows the average approval time on Apple's app store (regular submitting process) - http://appreviewtimes.com/