The blend path follows based on an objects arrangement.

I'd make the first object set to back, keep the 3 were it is, and make the last object set to front. (Object>Arrangement>Front to Back/Back to Front) Then Set the blend mode.

I don't know if it explains it, the arrangement is the same in both cases.
The bug occurs when I open the file, I see it and then if I mark one of the objects it "goes away", i. e. it "updates" to correct blend.

I don't think I understand what the "bug" is.

Well, sometimes Illustrator renders a different crazy blend (shown in second pic) out of nowhere, when it really should be -- and most times it is -- as shown in the first pic. There is no combination of arragements of objects done in usual way which can produce the same "fattening" effect that occasionally occurs and which I want to take advantage of

This in other words is (normally) impossible in Illustrator:
http://www.imgdumb.com/images/776599bug1.jpg

It took me a few looks but I finally noticed your "bug" the odd shape of the first blend between the first object and the 3, correct?

I would say, to a degree this "bug" can be reproduced. Notice the path that the blend is set to, though it's a non-stroked path, it still acts like any other path in illustrator. Meaning you can adjust the end points and the actual path, maybe by adding curves (which would change the angle of the blend in an abnormal way.) You might even try adding other path based filters (such as the zig-zag) and vary the blend mode (smooth blend to specific steps).

I found a way to reproduce the same effect in Illustrator alone, without the blend function
I'm not going to tell how until I have finished exploring it in my work, but something tells me Im not the first one to discover the technique =) ?

http://www.imgdumb.com/images/716182drgs1.jpg
http://www.imgdumb.com/images/166963drgs2.jpg

> Well, sometimes Illustrator renders a different crazy blend (shown in second pic) out of nowhere

Blend is based on outline interpolation. Strange transitions may happen when the paths are not compatible: different number of nodes, different starting points, or different path directions.
In Illustrator, path direction is controlled in the "Attributes" palette.

The two pictures in the first post are of the exactly same file. The buggy blend apears right after I have opened the file, and switches to correct blend when I "touch" , f eks. mark some of the objects
So , i don't think it has anything to do with path direction or whatever