Q:

Are there reactions where the stirring direction would make a difference?

I'm not a chemist. I don't really do anything with chemistry, so I know little of the subject.
I know a bit about chiral molecules. For example, I know that homochirality can affect light polarity.
I'm just curious: Are there chemical reactions where the direction of the stirring (clockwise vs. anti-clockwise) would make a difference? A simple explanation would be appreciated.

A:

No, for three reasons:
Firstly, you need a relatively large molecule and/or a high viscosity and/or a strong shear/extensional flow, before the molecule even notices that it´s in a nonuniform environment. The molecule, if it has an elongated form, will then align perpendicular to the normal vector of that flow field. That only occurs for sufficiently concentrated solutions of polymers, or liquid crystals.
Secondly, you need three vectors to be able to differentiate a left and right hand. You only have the normal vector of the flow field, and the preferred direction of your molecule. Or in other words, your reaction will be indifferent to you watching it from the top of the beaker or through the bottom. ;)
Thirdly, to get a third vector into your system, you need the normal of the flow field to change significantly, in a specific direction (using, say, a propellor instead of a stirring bar), on the lenght scale of your molecules. That is impossible with a macroscopic stirrer.

A:

In short: if the direction of stirring were a both reproducible and highly significant parameter for the synthesis of chiral molecules, the manufacturers would offer a back- and forward direction of stirring by default all across their stirrers.  But no, I'm not aware that there is such an effect.
Note, however, beside the stirring plate in the (small scale) lab driving a magnet in the beaker

(reference)
larger scale mixing uses overhead mixers.  These look similar to a drilling machine and a replaceable, axle-mounted propeller:

(reference)
These occasionally have the option to alter the direction of stirring, but only because the mounting of the stirring blades may be chiral, screw-like (examples).
Side note: At best of my knowledge, there isn't a significant and reproducible influence of the geographic position (latitude), either.  Thus, the synthesis of and with chiral molecules is independent if performed in Boston (northern hemisphere), Perth (southern hemisphere), or Quito (almost equatorial).

A:

These two intriguing papers conclude chiral environments can be induced by directional stirring, where the direction of the chirality depends on the direction of stirring.  And other work has shown that chiral environments steer the direction of chiral synthesis.*
So: If [direction of stirring] -> [direction of chirality of environment] -> [direction of chirality of synthesis], then the direction of stirring could affect chiral synthesis.
https://chemistry-europe.onlinelibrary.wiley.com/doi/full/10.1002/cphc.201200003
"Recently, several reports have suggested that the vortex flow of a solution of an achiral molecule gives rise to a CD signal, which is dependent on the stirring direction. This article introduces types of molecular architecture and material designs that show stir‐induced chirality....Supramolecular assemblies can be deformed to a chiral structure in a vortex flow which shows a CD signal even if the assemblies are achiral. ...Recently, we have shown that the stirring‐induced chirality caused by the host can be transferred to an achiral guest alignment. If such a transfer of chiral information could be realized on a molecular level from the vortex flow through a supramolecular aggregate to individual molecules, the consequences will be useful to a broad field in science and industry."[1]
[1] Okano, Kunihiko, and Takashi Yamashita. "Formation of chiral environments by a mechanical induced vortex flow." ChemPhysChem 13.9 (2012): 2263-2271.
https://chemistry-europe.onlinelibrary.wiley.com/doi/full/10.1002/chem.201100713
"This article introduces types of molecular architecture and material designs that show stir‐induced chirality.....Here we report that a solution of an achiral cationic gelator can vicariously transfer the macroscopic chirality of the vortex stirring towards an achiral molecule (in fact, a molecule showing racemic conformations)." [2]
[2] Okano, Kunihiko, et al. "Emergence of chiral environments by effect of flows: The case of an ionic oligomer and Congo red dye." Chemistry–A European Journal 17.34 (2011): 9288-9292.
*See for instance the following, which shows an example of how a chiral environment, created by a chiral solvent, "steers chiral synthesis":  https://cen.acs.org/synthesis/catalysis/Solvent-steers-chiral-synthesis/97/web/2019/07

