The Milky Way is quite big as galaxies go, at about 100,000 light years across. Consider that the Andromeda Galaxy is the nearest spiral galaxy and it is 2.5 million light years away. The size of the galaxy compared to the overall distance between us makes the distortion pretty insignificant. Muddy the waters a bit more with the fact that galaxies are generally moving away from each other and you really will make your head spin!

On the other hand, discerning individual stars in distant galaxies is pretty sketchy at best. The Hubble telescope has made it easier in recent years - but we're still only talking about the closest clusters.

So do we know the exact shape of a distant galaxy? No. At best we have a snapshot of roughly how it was, but not all at the same time! This is true of everything we observe - it's just exaggerated at cosmic scales.

 Like you say individual star positions within a galaxy will be off from their true relative held galaxial position depending on the galaxies rotational speed; For a galaxy like ours, star positions will be out by up to 100 light years if it were viewed approximately edge on, but considering our galaxy is 100,000 light years in diameter stars would only be observed up to 0.1% from their true relative galactial position which visually isn't very significant,  while visual distortions to the actual form and features of an observed galaxy (for example its spiral arms)  would be even more negligible, because stars within particular parts of the galaxy would have similar rotational speeds.  So basically, a galaxies diameter isn't large enough for the stars orbital speeds relative to the speed of light to make visual observations notably erroneous.