The willingness to overlook bad science in science fiction is exactly like the willingness to overlook any other kind of bad writing. Whether any particular lapse is gross enough to make you reject a particular work of fiction or drama depends both on the magnitude of the error and on the presence (or absence) of other good things that compensate. All of which brings in individual judgments, with enormous variety in results.
Still, it seems especially perverse (no matter how common the opinion!) to claim that bad science is not bad writing in science fiction. Which brings us back to the great debate over what is and is not science fiction. It's easy to slip into thinking that dumb, fake science means its not science fiction or is some nonexistent thing called science fantasy. A definition of science fiction that rules out changes in scientific knowledge or simple human errors would be absurdly ephemeral, and not much use. To say that Frankenstein was science fiction when Mary Shelley wrote it but now it's a fantasy because we know how absurd it is would be nonsense. To define science fiction as a type of fantasy because the vast majority of science fiction is boys' adventure stories instead of sober speculation (that comes true!) is the same error!
Science fiction is that fiction or drama with fantastic possibilities (hence, not realism,) including such things as alternate histories or fictional science. The better the rationalization of such things, the better the writing. But science fiction is not defined by the quality of its writing, nice as it would be to define one of my favorite kinds of reading as "The Good Stuff." The science fictional mode is one where all the characters have the same experiences and could potentially do the same things, live by the same laws of existence, whatever they may be. Everybody is equally material, and potentially equal in significance and power. Everybody's actions suffer the same restraint of natural law in the fictional world. Whether the rationalization of this world is well or ill done, whether the work relies on readers' previous experience of rationalizations in predecessor works, whether the rationalization is entirely fictional is irrelevant.
In the fantasy mode, there may be exposition of lore or some such, and rigorous plotting from the fantastic premises. The setting may deeply detailed, marvelously self consistent with the fantastic premises. Or the lore can be assumed to be the readers' common knowledge, the setting is a jumble, and the in universe handling of the premises. The first is not science fiction, or science fantasy while the second is the unicorn itself, Fantasy. Fantasy, in some fashion, is off from our world. To borrow a word, the fantasy is orthogonal to our universe. But the characters are different, because some are magic and others aren't. Some characters have a different relationship to the universe than others. Some characters can possibly do things others can't, for causes intrinsic to themselve, and their powers are not something anyone else could be imagined to have. This style of writing is entirely different. The closest science fiction comes to fantasy is the superhero story. That is why the superhero story is easily the most adolescent, if not outright juvenile, of the unique science fictions genres. (That especially includes the modern superhero stories which so greatly emphasize sadomasochistic sexuality.) Is there any adult who becomes enamored of a superhero? Without the gentle glow of nostalgia, who enjoys the superhero comic?
In the horror genres, the mode of the fantastic is irrelevant to the genre's fundamental aim. Obviously this is the case in horror without a fantastic element. When the irruption of the uncanny into the fiction is itself the source, the mode of the uncanny's origin, supernatural or natural, is a minor detail. So many horror stories use fantastic elements as the uncanny, horror is often lumped with fantasy or science fiction. That's because, for marketing purposes, there are many people who resist the fantastic in their fiction. (A feeling that leads many people to reject all fiction on principle.) If a horror story's uncanny is science fictional, a soundly rationlized uncanny is better than a badly rationalized one. Noting that is like saying that a horror story that doesn't use too many passive verbs is better. Yes you can think of the rare exception. But as a rule of thumb it's blindingly obvious. Or should be.
There are four other modes in which the fantastic is not explicated. One is the fable or fairy tale. The thing about fables, whether the traditional talking animals or fairy tales, is that they have very realistic types of people. Little Red Riding Hood and Reynard the Fox have names and realistic personality traits though they are not characters even in the way that Ralph 124C+ was. The fabulous background, whether talking animals or fairy godmothers, doesn't need rationalization, because fables and fairy tales are about the way people are (whether the moral is explicitly stated as in Aesop) or about what people hope for, but cannot allow themselves to dream about in their own persons. The fantastic is a screen, partly transparent, that highlights its subject by veiling other aspects of the scene. To put it another way, it allows daydreams or dilemmas that might be too painful to entertain seriously for oneself. A girl's hopes and fears for Cinderella are easier to deal with than her own hopes and fears. It is easier to imagine the little boy being honest than to look for the emperor's new clothes in daily life. In real life, the emperor has police. One of the rare modern blends of science fiction and fairy tale mode is Star Wars. Although an unambiguous commercial success, it is not an artistic success with high culture critics. It is severely criticized by even its ordinary fans. I think this is because Star Wars is a blend of fundamentally incompatible modes, raising expectations inevitably disappointed, engendering the hostility from the people most committed to one aspect of the series.
Another mode, the mythic, has unrealistic types, acting in strange and inexplicable ways. Yet myth is a genuine commentary on reality. It is not a playful "what if?" Hades' acquiescence in Persephone's return to the Earth for six months because she ate six pomegranate seeds is inexplicable. No person acts like that. But the story of summer and winter is a vital part of our real lives. However, fable/fairy tale and myth are generally short form works. And in any event they are less common now, because with the advancement of real knowledge the fantastic explanations of myth or the fantastic backgrounds are well known not to be so. That's why fables and fairy tales tend to be for children, who don't know much. The mythic mode tends to be rather self consciously stylized, reverential, a kind of authorial ejaculation of ambition. Explaining yourself is not impressive. Myth is also commonly used as a more or less conscious alternative to quotidian fact and logic. In this case, in universe rationalization counters the objective of myth. Myth is commonly used for other forms, notably the Homeric epics or modern fantasies, such as the juvenile series by Rick Riordan.
There is another mode in which the rationalization of the fantastic is irrelevant, which I suppose could be called the modernist. In this kind of works, fantastic things happening is a metaphor for the irrationality of the universe, or society, or the human soul. This shares with the horror genre the relative unimportance of the precise mechanism of the emergence of the irrational. This mode might be considered a metaphysical kind of horror. I tend to find these less satisfying because real people do tend to make sense of the world/society/themselves, or try to. Usually there are whole systems of ideas that attempt to explain the world, society and humanity, even if they are mistaken or are distorted to serve the ruling class. This mode tends to assume the horrific irrationality, then write strange and fantastic events to which people do not or can not find logic or meaning. Assuming the conclusion is a logical fallacy.
Last, there is the metafictional mode. Superficially, the "explanations" which may be proffered, like Jasper Fforde's numerous footnotes, serve as in universe rationalization. They are in fact commentaries on fiction as such. This mode tends towards either humor, as in Fforde or some sort of post-Modernist ideology.
One thing that is often unnoticed I think is that it is easy for the fantasy mode to blend with fairy tale/fable (in particular,) the mythic, the metafictional modes. This is because the fantastic elements, not needing explication, are more easily detachable. The science fiction mode can be more easily blended with the realistic mode, though even in a James Bond spy thriller, a science fiction element like lasers tends to be noticeable. The real difficulty appears to be when either science fiction or fantasy are not modes of specific genres, like military sf or sword & sorcery. In fictions where there is no playing with the formulas of the genre, no teasing about delivering on the emotional payoff promised by the form, either the science fictional mode or the fantasy mode, the media by which the fantastic is incorporated, becomes a message in itself. This is where the importance of identifying the mode is greatest. The modernist fantasy, which assumes irrationality, is incompatible with the science fiction mode.