MacOS – Applications stop responding when waking up from sleep

I would try adjusting your procedure. Since as noted the quoted steps provided below in practice are causing you to unintentionally wake the Mac from sleep in step 3, which may also problematically be waking it from sleep before it finishes going to sleep in the first place. So in a sense you were telling your MacBook Air to go to sleep and while your at it wake up from sleep, remove a display and all this other stuff at the same time. That may be the cause of the freezing, the shock of all the external devices getting removed while in sleep or while the mac is going to sleep.

1. Move mouse to HotCorner to put monitor to sleep (I do this instead of closing the lid since Lion has lid closing assume the external is taking over as primary display)
2. Close lid to put computer to sleep
3. Disconnect cables (power, display port, usb; maybe ethernet and audio depending on location).

USB activity as noted in Mac OS X: Why your Mac might not sleep or stay in sleep mode is a perfect way to wake your mac from sleep.

I would recommend doing the following instead:

1. Save your important files and data in open applications in case things go wrong.
2. Disconnect cables (power, display port, usb; maybe ethernet and audio depending on location).

3. Wait for you mac to recognize that the external display is disconnected, usually screen fades to blue for a few seconds, before going back to normal view of your Mac. etc.

4. Close lid to put computer to sleep or choose Apple > Sleep, etc...

5. Verify the sleep indicator light is slowly pulsing, before placing the MacBook into any case.

So ya try this out and see if it stops the random freezing. If it does not then there may be other hardware / software problems at hand, check your system logs, etc.

Realised I answered a dupe of this here: How can I download something with display turned off (Ctrl+Shift+Eject)?

My answer to that question below:

I always use this combo as well, however this does not immediately sleep my machine in ML.

I believe this is a separate issue at play here. According to Siracusa's ML review, unlike in previous OS X versions, in 10.8 your system is eligible for sleep immediately upon "user inactivity" (the inactivity delay being set in your energy saver settings) unless the currently running apps make "power assertions".

In this case, that key combo is signalling to the OS that "user inactivity" should be triggered right away. In such a case, if your particular app that's downloading stuff does not make power assertions, your system will sleep.

I have come across the same issue generally (not necessarily related to triggering the screen sleep combo). See: Mountain Lion sleeps too aggressively