Again, please inform me if this affects other versions.

It is possible to have a double chest where one chest is facing north while the other is facing south, but they appear to be the same orientation.

See the attachments below.
Fig. 1: Two chests, one block apart
Fig. 2: Setblock command to place a chest in between them.
Fig. 3: Three chests in a row, with me looking at the third invisible chest.
Fig. 4: The third chest is broken and replaced with a block (not necessary to place a block) and another setblock command is shown (same command as in Fig. 2)
Fig. 5: One chest faces north...
Fig. 6: ...while the other faces south

This shouldn't happen, as the chest facing north should really be facing the same way as the chest facing south. But for some reason, the chest's state doesn't update.

If you set both chests to an angle 90 degrees from what they should be at, you'll get a graphical glitch. In the screenshot, the original double-chest was pointing east-west, and both chests were /setblock-ed to point west.

Edit: Simply placing a double chest then using a /setblock command to place a chest facing the other way will duplicate the bug.
e.g.
place a chest at (9,39,2)
place another chest at (8,39,2) to create a double chest
/setblock 9 39 2 chest
One chest faces north, the other faces south, yet they appear to be the same orientation.