Does it matter which way Torbjörn's turret faces?

I will have to say it does matter which direction the Turret is facing. The turret will default to the position it was facing when first created, so there will be a slight delay between a forward facing turret and a backwards facing turret when an enemy is in LOS.

Although given discussions on rebrn, it seams the rotation speed is near instantaneous, but not 0, so it is a matter of milliseconds.

For Pro players, it probably matters, but for the casual bunch it shouldn't.

EDIT: As per further request, and of course my bad for not adding this, here is how fast the turret rotates 180' It clearly takes some time and is much better to have the turret facing the enemies, than having it turn away after a clutch.

Judging by the video and Youtube's .25 play speed. It took a second for the turret to rotate 180'(MAYBE 1.25 seconds).

Torbjorn's turret instantly detects enemies and if there's a turn speed, it hasn't been noticeable to me. Therefore, you shouldn't need to worry about which way the turret is facing when placing it.

Yes, there are advantages to certain orientations of the turret during placement, although they are fairly minor. The specifics of this depend on what you're trying to accomplish with your turret. There are two main approaches to this that I've seen.

Out in the open: The turret is placed near an objective or chokepoint so that it has a large field of view to engage enemies. This also means that it will be in plain sight, so it's up to your team to keep the enemy focused on them rather than your turret. In this scenario, there's a small benefit to pointing the turret toward the locations that enemies are most likely to appear since it negates the brief (but not entirely negligible) rotation speed that occurs before it can begin firing at the enemy. This answer does a great job of examining the rotation speed of the turret, so I won't go into that any further.

Tucked away: The turret is placed somewhere that isn't immediately obvious, such as in a side room, with the intent of surprising the enemy. One tactic involves placing the turret on a health pack, which will not only heal the turret if it takes damage, but also increase the likelihood of finishing off an enemy that was already low on health and in need of the boost. Since the turret projects a laser that is visible to enemy attackers, pointing the turret toward a location that enemies are likely to come from can give away its position. This can allow enemy heroes to avoid the trap or destroy the turret before it can fire at them (particularly in the case of heroes such as Junkrat or Pharah who are capable of splash damage). In this scenario, it is more advantageous to point the turret into a nearby wall so that the laser will not be noticed by the enemy until it is able to fire at them.

In either of these two cases, I would consider these advantages to be fairly minor, but they can make a difference if you're trying to optimize your placement. I hope that helps!