In general (not restricted to this site), what counts as a good philosophical explanation? Are there any objective standards?
Its generally accountable to the philosophical community who over time have generated certain critical standards; its in relation, or rather dialogue to this authority that ones own thought becomes critical & authoritative; this is one one reason to signpost readings of either the primary or secondary literature; and this is often reflected in style.
This doesn't mean that the canon of philosophical works become a 'dead weight' but that they're used to draw up a map & orientation; one also becomes aware of the vast weight of previous argumentation and their repercussions on the cultural firmament of the time.
For example Hannah Arendt uses the phenomenological orientation of Husserl & Heidegger to orient her understanding of political science - this looks at philosophy as being in the world as opposed to from sub specie aeternitas (from the viewpoint of eternity). She counters the valorisation of Platos contemplation with action in the public sphere - ie politics and this draws on her understanding of how politics was understood in the Greek city-state.
Another example would be the Anglo-American analytic tradition which though in a narrow sense was stimulated by the logical argumenation and rigor of Russel, Frege & Wittgenstein; in a wider sense it is derived from the the style of argumentation in Plato where clarity in thought is seen as a natural good; and this is filtered through the European Enlightment tradition.
What can be called the counter-Enlightment takes its orientation with artistic Romanticism; its exemplars are Nietzsche & Derrida amongst others. Their writings tend towards contradiction, polemic and obscurity; their work resists easy reading as the thought is concealed. One can consider it as a code that can be broken in several ways or creatively 'misread'.
And their are the isms that help orient writers in the larger picture and thus orient in what way they are in dialogue with each other; a philosopher doesn't belong to a certain school; more that one should see these isms as a prism that overlays their writings and refracts it in many different directions; whereas seeing the influence of their philosophical predecessors turns their texts into a kind of palimpsest.
All this isn't just true of philosophy, but of any scholarly tradition; and is true of the sciences - say Mathematics or Physics. One could ask of a more particular methodology; in the physical sciences for example there is the notion of the 'repeatable experiment'. But there is no such empirical inquiry - but the larger sense of observation is important; and thus, for example Arendt relies on testimony (and what is this if not observation?) filtered through the secondary literature to examine the notion that she calls Totalitarianism in her book of the same name, as a political institution in its own right - through its roots and its future; and how it is in fact characterised.
As you probably know philosophy is centered on asking and answering three fundamental questions, the most fundamental being "what is there?". With "how do i know?" and "what do i do?" the latter two questions necessarily arising as the inquirer becomes self-conscious of the first question, which translate into the philosophical fields of metaphysics, epistemology and ethics respectively. Good philosophy can be said to be based on the most logical possible way of answering the first question, which said answer, by extension provides a framework to answer the latter two questions. This type of "good philosophy", is good because it is logically self-consistent, that is, it does not contradict itself, and is superior to philosophy which is self-contradicting and inconsistent with logic, that is, in this respect, "bad philosophy" is self-evident".
That being said, because Philosophy has not yet produced a theory of everything which adequately satisfies the answering of the three fundamental questions in the most logical and self-consistent way possible, every philosophy that exists, is inferior in this respect to the best possible philosophy.
Now as to why you've observed fairly dubious "philosophical" explanations, that are still highly rated and accepted as answers. The answer to this is because this site is very dogmatic in its approach to answering questions, that is, this site is designed as a platform of which to provide answers to philosophical questions based on the existing work of philosophers. Basically answering these questions using the words of other philosophers, and answers are more highly rated not based on them being logically correct pertaining to the question, but more so based on a specific philosophers thoughts on a question, and the justifications as to why said philosopher thought this or that in regards to this specific question and answer. This is how "dubious" answers become highly rated, because the answer isn't necessarily the correct answer to the question, but a specific philosopher's answer to the question, and said philosopher doesn't necessarily provide the correct answer to the question, just a philosophical framework of which helps the question asker better think through the problem.
My own "Intro to Philosophy" textbook said the following:
Truth, Profundity, Clarity but the greatest is Clarity
Truth is of course as elusive a concept as anything else discussed philosophically, and wouldn't be how I would have expressed it, but the basic idea it that the arguments are strong: the arguments (at least appear to be, even after thinking through them considerably) logically valid as well as based on plausible premises. Does it seem correct to you? (Be honest, really.) Would it seem to correct to others? That's the best we can do, for now.
Personally, I'm not sure if I would have put profundity in the list, but I'll admit that it's nicer to have lists of threes. The fact is though, is that good philosophy should make you think in ways that you haven't thought before.
The greatest is definitely clarity, at least for me who grew up in the tradition of analytical philosophy. When philosophers make seemingly profound statements, or pithy aphorisms that might do better as bumper stickers, one might initially be drawn to their elegance, before thinking about what the phrase really means. Some of the most elegant phrases, upon analysis, are revealed to have no meaning at all.