As far as current objections to final causes are concerned, I cannot point to any authors. I guess everybody simply thinks final causes are dead and buried. (To the contrary, I can point out a few current authors who argue that final causes are back with a revenge.)

When the times turned modern, objections to final causes have involved pointing out that there is too much supernatural or unempirical in them (as in statements like "this is how God made it" or "it serves nature perfectly"), too much subjective or vague in them (as in appeals to harmony or beauty) or that they do not seem like causes at all, but more like explanations with no necessary relation with causality (as in answers to most why-questions).

I personally think that the framework of four causes is an Aristotelian peculiarity that does not serve everybody equally well, and possibly arises from some translation problem http://www.borishennig.de/texte/2016/fourcausesbk.pdf

Boris Hennig wrote:

Aristotle says that in order to really understand a thing, we need to understand its aitia, and he distinguishes between four kinds of aitia. This term, aitia, is usually translated as “cause”. However, not all of Aristotle’s four aitiai are causes in the modern sense of this word. Perhaps none of them are.

The common object is that irreducible dispositional properties would involve an intentional relation to a non-existent object. Intentional non-existents are a major worry for philosophers working with mental intentionality, one which many find more disturbing when the object doing the intending is not even consciuess. Armstrong discusses this objection somewhere as does George Molnar.

https://plato.stanford.edu/entries/dispositions/

In very basic terms I think the objections to final causes remain the same. They are that final causes are unnecessary to understand causality and contrary to parsimony, and that they ill-fit a naturalistic understanding of the world. Most of the different objections, in different times and places, are variations on these.

DanielCC wrote:

RomanJoe wrote:

DanielCC wrote:

The common object is that irreducible dispositional properties would involve an intentional relation to a non-existent object. Intentional non-existents are a major worry for philosophers working with mental intentionality, one which many find more disturbing when the object doing the intending is not even consciuess. Armstrong discusses this objection somewhere as does George Molnar.

https://plato.stanford.edu/entries/dispositions/

Why is this seen as disturbing? Do they think it entails something along the lines of panpsychism?

No, they suggest it entails non-existent objects 'having being' in some way. How can one stand in relation to a non-existent object? Powers theorists are fine to resist panpsychism as they reject the restriction of intentionality to the mental. 
 

 
Doesn't that beg the question against the fifth way, though? Part of the argumentation for the fifth way is that dispositional properties are intended towards objects that do not exist or do not exist yet, but since the disposition is there it must be explained by a divine mind ordering things (for instance, by having the intended objects in its intellect)