So this has been covered elsewhere (and in exhaustive detail on this XDA thread), but for those of you who have been suffering lag on your Nexus 7s, 4.1.2 fixes the problem. It seems likely the issue was caused by missing TRIM commands to clear storage that had been used and then subsequently freed up on some 16GB Nexus 7s that use Samsung NAND (some of the 16GB N7s use Hynix NAND, and so don't suffer from this problem), and TRIM has been implemented in the software in 4.1.2 where the OS seems Samsung NAND.
However, just updating to 4.1.2 won't fix the lag problem if you're experiencing it. The system needs to see the space filled, and then emptied so it knows that it has to properly clear the space and prepare it for fresh writes. You can do this manually by filling the space with.. whatever. MP3s, video, garbage zip files, then deleting them manually. The XDA thread above has some command line options to do this, as well, but the easiest way I've found is to use Forever Gone to fill the storage and wipe it. The app's actually designed to do a secure delete by filling and wiping storage, but it works for this purpose, too. I just finished performing this on my N7, and while I got a reset when I had only 150MB free, I was able to restart and completely fill and wipe my storage. My tablet wasn't suffering lag after a hard reset a few weeks ago, but I did notice a jump from 83.31 IOPS to 127.46 IOPS after the wipe (in Androbench), which may make a difference. If you've been suffering from lag, this is worth doing after you've received the update.
TL;DR:
To remove lag after receiving 4.1.2 fill storage completely and then free that space back up.
However, just updating to 4.1.2 won't fix the lag problem if you're experiencing it. The system needs to see the space filled, and then emptied so it knows that it has to properly clear the space and prepare it for fresh writes. You can do this manually by filling the space with.. whatever. MP3s, video, garbage zip files, then deleting them manually. The XDA thread above has some command line options to do this, as well, but the easiest way I've found is to use Forever Gone to fill the storage and wipe it. The app's actually designed to do a secure delete by filling and wiping storage, but it works for this purpose, too. I just finished performing this on my N7, and while I got a reset when I had only 150MB free, I was able to restart and completely fill and wipe my storage. My tablet wasn't suffering lag after a hard reset a few weeks ago, but I did notice a jump from 83.31 IOPS to 127.46 IOPS after the wipe (in Androbench), which may make a difference. If you've been suffering from lag, this is worth doing after you've received the update.
TL;DR:
To remove lag after receiving 4.1.2 fill storage completely and then free that space back up.