Using filters on view changes order values

I've attached two pictures. Picture 6 shows the order values before the user filters the view. Picture 7 shows the order values after the user filters the views. I think changing the filters should not change the order values.

Yes, you're right. That's just the way it works. I also thought about this effect a long time.
I ended up with:
Filters should only be used if nodes don't appear more than once in different filter states. In this case you actually use filters to split the view in many logical derived views.
If you want to filter the content without any restrictions you may not use DraggableViews for this display.
I'll mention this in documentation.

How do you think about this point of view?

I'm not sure I completely understand, but let me see...

How about this: the Order value is set by people who have the permission to set it. The sorting OF those values is set by anyone with access to the filters, and is displayed only to that person who set it. Other people start off with the default sort.

So let's say I have

item 1 - order value 1 - category A
item 2 - order value 2 - category A & B
item 3 - order value 3 - category B
item 4 - order value 4 - category B
item 5 - order value 5 - category A
item 6 - order value 6 - category A

The default sort is on the order fields, ascending.

I'm a user, I come along and filter by category so I see only category A.
I see:
item 1 - order value 1 - category A
item 2 - order value 2 - category A (& B)
item 5 - order value 5 - category A
item 6 - order value 6 - category A

I can sort that list any way I want, by order field, or if allowed, by clicking columns to sort by other columns, and it will NOT affect the order value. Thus it will not affect any other users.

Then if another users filters by category B they get:

item 2 - order value 2 - category (A &) B
item 3 - order value 3 - category B
item 4 - order value 4 - category B

and they in turn can sort however they want.

I'm probably not understanding something crucial, but I think my way might work. Otherwise, please add in a second order field that WOULD remain constant and act like what I am suggesting.

This is a great module, I really appreciate it. Thank you!

documentation, right?

No, I don't think documentation will do it - at least for me.

I resolved it by switching to the node-order module.

I still don't know what you want to be improved.
Saving an unique order for each kind of filtering..simply doesn't make sense.

If you change the view (and this is the case when you use filters) then you change the order values of the nodes.