How to perform full check of ext4 file system structure?

As mentioned by Satō Katsura, run e2fsck in "force" mode:

e2fsck -f /dev/sda2

This will force a check even if the system thinks the file system is clean. The "verbose" option is helpful too:

e2fsck -vf /dev/sda2

As a side-note, and not applicable in your case, but if you use LVM for your storage you can use the neat little lvcheck tool to run an "offline" file system check on a mounted file system (it uses an LVM snapshot and updates the file system metadata if the check doesn't find any errors).

Also, you could add the -y flag to avoid answering questions.

From the manual:

-y assume an answer of yes to all questions; allows e2fsck to be used non-interactively.

So extending the answer (since I cannot comment yet) from @Sato - you could run:

e2fsck -vfy /dev/sda2

sudo touch /forcefsck
sudo reboot