When a discrepancy between theory and observations is found, scientists devise possible explanations for it. These explanations are then tested via observation to see what holds up and what does not. The theory is thus improved, and science progresses. Dark matter has been the most successful explanation so far. Modified gravity is the leading contender, but thus far hasn't been able to make predictions that would confirm it over GR/DM that have been verified observationally.
But let's assume that dark matter is incorrect, what then do you propose as the solution to the problem? Do you think a modification of our understanding of gravity is necessary (an even more contrived solution by your reasoning)? Or do you think there is not a problem in the first place -- galactic rotation curves are wrong, velocity dispersion data is wrong, gravitational lensing data is wrong, Bullet Cluster observations are wrong, CMB observations are wrong, ΛCDM model of cosmology is wrong? That's a lot of evidence to go against.
But hey, if it's the latter, help demonstrate it to the scientific community. You might get a prize for your work!
And how exactly is the speed of the Sun's revolution measured? It's probably been inferred by the rotation of other galaxies rather than directly observed. Which means that we're not even sure exactly how much dark matter would be needed to keep us in the Galaxy.
Instead of assuming that you know how astronomers figure things out, try reading up on it for yourself. A
quick search on google scholar or
ApJ might have helped you there. I think this excerpt from one of those papers is quite noteworthy:
Positions of Sgr A relative to the background source J1745-283 for epochs spanning 2 yr are plotted in Figure 1 with open circles. They indicate a clear apparent motion for Sgr A* relative to J1745-283, consistent in magnitude and direction with the reflex motion of the Sun around the Galactic center. The positions in the east-west direction have typical uncertainties of about 0.1 mas, as estimated from the scatter of the postfit position residuals about a straight-line motion. It is interesting to note that, while it takes ~220 Myr for the Sun to complete an orbit around the Galactic center, the east-west component of the parallax from only 10 days motion can be detected with the VLBA!
Yep, we can actually see the parallax effect from the sun's orbital motion over a period of just 10 days.

The problem with Astronomy is the one observer problem. You have one eye, the solar system, to study the entire cosmos, and you cannot move that eye. Therefore we are prey to optical illusions, error, and geometric limitations. We may make many telescopes on the earth and even launch them into space, but such differences of distance are nearly meaningless when observing other galaxies.
We can't trust the results of astronomical observations because we're stuck in one place? So what? The light from the whole Hubble Volume constantly falls on us, and we are constantly studying it, making theories, and testing those theories against that evidence. Maybe the whole universe is lying to us, but I think that would be a pretty ridiculous philosophy to hold.
As for errors and whatnot, astronomers can and do account for this just as any other scientist does. Optical Illusions? You mean like gravitational lensing? Geometric limitations? Sure, we can't see galaxies blocked by the dust of our own galactic disk. Differences of distance? So what? There is the cosmic distance ladder.
edit for typos