We have no way of knowing how near “the end of the road” we are in any given area of inquiry. We don’t know what we don’t know. That said, I think it’s pretty safe to say that science didn’t get it wrong when it comes to heliocentrism. Vaccines generally work pretty well too, so I think it’s also reasonable to conclude that science got it mostly right when it comes to the immune system and germ theory. That’s not to say we’ve discovered all there is to know about these things, but it is to argue blanket statements regarding science getting it wrong are totally inappropriate given its success so far. You do give a nod to these achievements, but still seem rather ambivalent.
It is true that science is an approximation to a very large extent. More so in some areas of inquiry than in others. However, being approximately right is different than being dead wrong. Right and wrong aren’t as binary as the general public makes them out to be.
Science isn’t nearly as wrong nearly as often as, say, astrology or reading tea leaves. The methodology is actually quite sound. You seem, toward the end here, to begin leaning toward Isaac Asimov’s position that what matters isn’t getting it perfectly right, but how relatively wrong we are. See his wonderful essay The Relativity of Wrong for his full argument. If that’s your argument, then I agree with you. However, I’m still left wondering if you share his conviction that the scientific method actually works. Science isn’t in fact wrong all the time, but when you conclude with “science is indeed wrong…” I get the feeling you think it is nearly as wrong as any other human endeavor one might randomly choose to compare it to, or at least as likely to be.