Your question has some good answers already, so I would just like to mention one more facet regarding the wrongness of belief. Isaac Asimov wrote a wonderful essay, titled The Relativity of Wrong, that you might want to take a look at.
In short, even though everything we know may be wrong in some aspect, we can confidently state that we are less wrong today than we were yesterday, or 100 years ago, or 1000 years ago, etc. To take one of the examples used in Asimov's essay, what is the shape of the Earth?
While the answer 'Flat' is a useful approximation for short distances (the curvature of the Earth is close enough to 0 that it was very hard to measure by early civilizations), we quickly run into big problems describing our planet this way. This is a qualitatively wrong answer.
Answering 'Sphere' is a much better description, and our modern notions of navigation are firmly entrenched in the assumption of a spherical Earth. However, this answer is also wrong - at least in the sense of not being completely, absolutely, 100% correct.
'Oblate Spheroid' is a better answer again. Because the Earth rotates on its axis it bulges slightly at the equator compared to the poles. This is a much smaller correction than moving from 'Flat' to 'Sphere' - so is it fair to say that both answers are equally wrong? Is it not more fair to say that one answer is closer to the truth than the other?
After all, even the 'Oblate Spheroid' answer isn't 100% accurate, either. The southern hemisphere happens to be slightly 'bulge-ier' than the northern one, so to be even more technically accurate you would have to describe our planet as being ever-so-slightly pear-shaped. The difference between our planet and a theoretical oblate spheroid is so small that it took very precise instruments on a specially-designed satellite to detect.
So yes - everything we know will probably be shown to be wrong in some sense at some point in the future. HOWEVER, this does not mean that we will one day say 'The Earth is a cube'!
- Being 'wrong' in the sense of not being perfectly, 100% accurate is no reason to think that there's no value in being close or close enough.
- Being 'wrong' in this way does NOT imply that every possible explanation is fair game. The 'Tooth Fairy Theory of Dental Disappearance and Monitory Gain' isn't going to become an accepted explanation any time in the foreseeable future.
Now going back to your core question:
[If] anything we believe we know, at any point in history, could be wrong, why should we continue pursuing science?
- It is quite reasonable to strive to be less wrong tomorrow than we are today, even if we can never be perfectly correct.
- Science is a tool with a proven track record in helping us become more correct in our descriptions of our universe and the phenomena within.
- Ergo, let's keep doing science and see where it leads us! Let's continue to improve on our models, knowing that today's models are better than yesterday's models but not as good as the ones we might have tomorrow.
Who knows what mind-blowing, cool new thing is waiting for us just beyond the horizon of our current knowledge and understanding? What new questions are waiting to be asked? C'mon, let's go find out!