OP...if by "little pieces" you're referring to the four side mounts of the 6-pt mounting system, I've yet to encounter that issue with those specifically with my 350-CS. Now I did have a problem with both my towers ever so slightly coming loose after a string job and this happened on a few occasions. I saw no impact to the racquet or string job as the movement was very slight...but movement nonetheless. I removed both my towers and checked the bases of the towers very closely, etc, etc and found nothing that stood out...checked the turntable area as well and found no runout, no low/high spots from the casting, deviations, etc there. My remedy for this slight tower movement was blue Loctite on the threads when I set the towers back in place. I can't remember the exact measurement from the very ends of the turntable where I re-mounted my towers (they went right back in the same position as before the blue Loctite was applied to the threads). I think I mounted the towers, but don't quote me until I check again and get back with you after work today, either 1 1/2" or 2" from the end of the turntable to the backside of the towers closest to the turntable ends, for both towers. Where I mounted the towers will accommodate all racquet sizes from 85, 95, 97, 98, 100, 105 sq in without the need to move the towers again (never mounted anything larger than 105 sq in but I'm sure the Loctited tower positions will be fine for larger than 105 racquets as well).
My towers have not moved since cranking them down using blue Loctite on the tower mount threads. And this could very well be related to where you're seeing 'side mount' loosening of contact with the frame, albeit my side supports were fairly snug against the frame during all stringing. As the side support pivoting arms are directly mounted to the towers, when the towers move they have to follow, they don't have any choice. Again, I never noticed any side mount loosening per say, but it could've been there the entire time with mine as well and never paid no attention to it. Check your towers and measure exactly from a fixed reference point (very ends of the turntable) and see if you get any movement/loosening before and after stringing. If that's the case, I would tackle the tower issue first and foremost.
Just a little FYI...if you do need to Loctite the towers in a fixed position, use blue Loctite only, do not use red Loctite. If you choose to use red, to get the towers to loosen in the future, you'll have to use heat and I'm not talking a gal's blow dryer either to get the tower bolts to break free from the nutsert that's pressed inside the towers that they tighten into...you may not like your finished paint job with the machine afterwards, so go ahead and invest in a can of white Krylon gloss or semi-gloss one because you're gonna need it.
I'll chime back later with the exact measurement/position my towers are located from the ends of the turntable. If this doesn't help, we'll resort to Plan B next, which I don't know exactly what that is shy of you sending me your machine and I'll weld every moving piece in place and that'll cure its' little issue once and for all. Lol
