Do you have an actual, specific proposal? I've yet to see anything concrete, not even in answer to specific questions I raised. This is the sort of thing that typically gets removed by moderators.

It would be nice if there were an option to Series so that it would give a correct Taylor series expansion when the expansion is done on more than one variable.

You're right. I'm talking about a feature that should have gone into Series when it was first introduced (or a separate function created), not the changes in the most recent version.

Yes this was by design. It might help to look at the input forms to see why it is useful.

the first example is a straightforward Puiseux series in sqrt(x).

InputForm[Series[Exp[x]/Sqrt[x], {x, 0, 1}]]                            

(* Out[3]//InputForm= SeriesData[x, 0, {1, 0, 1}, -1, 3, 2] *)

Translating from the origin to +1, would be:

InputForm[Series[Exp[x-1]/Sqrt[x-1], {x, 1, 1}]]                        

(* Out[4]//InputForm= SeriesData[x, 1, {1, 0, 1}, -1, 3, 2] *)

So we have the same series coefficients, we just shifted our base point.

The key point to realize is that fractional powers of (x-1) differ from fractional powers of(1-x). In not accounting for this, for a long timeSeries` did not behave well at branch points. The change below is part of several that were intended to address this deficiency.

InputForm[Series[Exp[1 - x]/Sqrt[1 - x], {x, 1, 1}]]                    

(* Out[5]//InputForm= SeriesData[x, 1, {1/Sqrt[1 - x], -(1/Sqrt[1 - x])}, 0, 2, 1] *)

This is a very different object. It has fractional powers inside the coefficients. While this is not so desirable it is vastly preferable to giving a result that would be just wrong in a nontrivial part of any neighborhood around the base point, which is what would result from pretending that Sqrt[1 - x] can be recast using Sqrt[x-1].

To get a "nicer" expansion one might restrict the domain to real x larger than 1, where such a rewrite can be done.

InputForm[Series[Exp[1 - x]/Sqrt[1 - x], {x, 1, 1}, Assumptions->1<x<1+ /1000]]                                                                         

(* Out[6]//InputForm= SeriesData[x, 1, {-I, 0, I}, -1, 3, 2] *)

I'm not sure if the order term is an issue of contention but I should state in any case that the attempt is to have the same "order" that would have shown up previously, provided we now account for coefficients that are "almost" fractional powers of x-basepoint, in particular, fractional powers of c*(x-basepoint) where c is some constant that is not positive and thus cannot blindly be pulled out of the radical (which was the error of the old ways...)