According to the Android Central forums, this issue was caused by missing TRIM commands that are supposed to clear storage that had been used and then subsequently freed up.
Apparently this problem only affected a subset of 16GB Nexus 7s that use Samsung NAND (some of the 16GB N7s use Hynix NAND, and so don’t suffer from this problem), but now TRIM has been implemented in the 4.1.2 update.
But just installing the update may not be enough to fix the problem, 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 withn files, for example MP3s, video, zip files, and then deleting them manually. Alternatively, the poster suggests using this app to fill and delete your free space.
Solution: To remove lag after receiving 4.1.2 fill your Nexus 7′s storage drive completely and then free the space back up again.
Has this worked for you?
I haven’t got the 4.1.2 update yet, knowing my luck I’ll be the last to get it, but will report back as soon as I’ve given it a go.
It will be interesting to see if this, plus the advise above, removes this annoying performance problem once and for all. The feedback on the forum seems promising, so fingers crossed.