Anyone have any idea why during the soviet training my tank turret wants to sweep from side to side after I have assigned a target?

It does the same sometimes, once a gunner, and order the driver to back away and the tank turns right and/or left as it is backing away. One has to take control of the driver's seat in that case. Sometimes it is also related to the fact that some people don't engage free view (or look). When you are in free view , your mouse does not control the tank behavior anymore, but just your point of view of the game. Disengage free view and your tank will move laterally as you move your mouse if you were sitting in the driver seat at that particular time.
A lot of those issues are wiped out when a team of human are being in controls of the tank.

I also noticed an issues with trees. Your tank barrel will not crush a tree but it will force your barrel in a direction as the tree is blocking it. I am glad they did not model the damage to the turret mechanism and to the gun elevation's mechanism

Another issue with the bathroom wooden shack on some house property, the tank bounces off it without crushing it. Pretty amazing actually!

It is endless as it was in Arma at its inception. I don't worry too much as historically a lot of those bugs were wiped out by patches or by individual player's fix.

From the OFP inception, VBS1, Arma, VBS2, ARMAII, they all had the same growth pattern, I would have been very surprised if IF44 would have been different.

And it will be the same with ARMAIII!

So, if it does not actually answer your question, don't be alarmed, it is normal!...Your tank won't be doing it anymore within a month or two!

Thank you for your reply : )

I'm not too worried about the bugs and whatnot. It was worse with Red Orchestra 2 for what seems like forever. I can tell a winner when I see it, though, so with all the features (BM-13 is my favorite) of IF:L I'm sure it will be great.

Affirmative!