PS - there's also weighting holes on the inside and rear of the arm.   CBR

Select Torso Mesh then shift-double click weight tag....   CBR

How do I see what you see?

That will no doubt help the rigging guys who will be able to tell you how to solve this. I am not an expert in this area myself, but I do notice that the parts of your torso that are glitching out when you move the arm has big holes in the weighting in that area (the black bits below), so would guess the problem is probably that.     CBR

@teknow   That will be great! Appreciate it! Looking forward!    I am currently doing some medical and scientific modelling for education. Amazing video and animation. Yes, absolutely, C4D is amazing when doing such animations.

Here is the file: https://www.dropbox.com/s/vzrkb0skpuokhlr/SPACE_SUITE-rigged.c4d?dl=0 I used C4D R19.

Glad I can help! I will post my first video made with my parametric DNA rig, DNA Helicase, tomorrow to show you what I am babbling about. Also, here's a gorgeous video by Eric Small and it shows just how fabulous projects can be using C4D:  

If you are interested in getting more out of procedural noises in C4D, this tutorial series is excellent.  https://www.fxphd.com/details/471/    It will predate v20's node based system but all the principles will apply.  Totally worth the buy.

@teknow   Thank you for your reply and sample files! Really appreciate it!     I will try to follow your steps. Will get back to you tomorrow if I hit any roadblock.   Thank you, again.  

It almost certainly is a weighting problem that persists despite your cleanup, but without the scene file we just can't tell where. Pls upload it. If too large, dropbox or similar...   CBR