Is it ethical for authors to reference another paper, but not cite it formally, because they consider it unscientific?

As editor I would not accept this in a publication. If it is published it should be referenced. Yes, it bumps the references for the authors and yes, bad science may attract a fair amount of citations for all the right?/wrong? reasons. But, it is not up to the authors to decide how referencing should be made, journals have guidelines that should be followed. Having the citation properly referenced makes it easier for others to find the article and see it for themselves.

Furthermore, from another point of view the statement that something is "unscientific" is not appropriate either. It is an opinion. The cited paper can be unscientific but the academic way to show this is not to just say it but to prove it.

Your quote is a specific case, of which I know nothing, so the reply concerns the general case but I would react if I saw something like that in a paper I edit and I would ask the authors to stick to facts.

One last point is that if a paper is really bad, then it should be considered for retraction. That is how scientifically extremely poor, bordering on dangerous, papers are handled.

"Citations are considered as a measurement of the impact of a paper, and as such, a proxy for its quality."

Many people, including me, agree that these considerations are not appropriate; the second even more so than the first. However, using a practice as you describe, i.e. citing a paper but not adding it to the bibliography, could work in the direction that citation indeed stand a bit more for "impact" and "quality". However, since are so many more flaws with the impact factor and bibliometrics as a measure for anything else than the number of citations (such as self-citations, citations "forced" by reviewers, citations rings in the vanity press, citing without reading the paper…) I would say that it does not make sense to use a practice of citing without citing.

My brother proposed a "markup" for citations which goes in the same direction, i.e. something like

\cite[negative]{PaperWithSevereErrors}
\cite[community feeling]{PopularPaperWithNoSpecificRelation}
\cite[please journal editor]{AnyPaperOfEditor}
\cite[enforced by a referee]{SuggestedPaper}
\cite[proof or evidence elsewhere]{TechnicalPaper}

but I guess that this proposal has to be taken with a grain of salt…

In another direction: Citations say on what work you build your own. If there is a paper which you find horrible and which you do not build upon, is there a need to cite it? If you simply want to bash some others work, use a blog post, or probably even don't do it at all. However, if you think that the respective paper is bad but used by others nonetheless and want to emphasize in what way it is flawed than you have to cite it properly as your contribution really builds upon that paper.

It's most certainly bad form. Let's say you read a paper that you believe is wrong, and you want to write a paper saying how wrong it is.

If you cite the paper, yes, the wrong paper will get the citation, but when people who know how to use the literature (less and less every year -- sigh) look up the original paper, they have a fair chance that bibliographical tools will point them to the new paper. This should help correct the literature, and prevent the wrong paper from being cited for years to come. The citations will eventually die down for the wrong paper.

In contrast, if you don't cite it, it will be harder for the community to learn that its wrong-- thus YOU ARE HURTING YOUR FIELD by not using every tool at your disposal to correct the literature!!

As to ethics, it's certainly not plagiaristic with the full citation appearing in the text. You're not trying to hide anything. It's just wrongheaded and somewhat petulant, but I'm not sure I would call it an ethical breach of real magnitude. It certainly doesn't make the author look good.