Take a look at this Proper Motion Simulator
. Click on the "Pleiades proper motion" link. Once you see the stars, immediately press the P key to pause the simulation. Now click the + button at the upper left to advance the simulation 1000 years per click.
As you will see, the Pleiades does not change much even over a span of several thousand years. So when we see it as it was when its light was emitted 450 years ago, we can rest assured that it has not changed much since then (at least not enough to notice unless you track it with great precision over a period of many years).
Even Barnard's Star, (the star with the fastest known proper motion) only moves a short distance on the sky each century. On the page with the "Pleiades proper motion link", if you click the "Barnard's Star" link you can play with a simulation of this.
Also, astronomers have a very precise understanding of the lifetimes of stars and galaxies, galactic rotation speeds, etc. and based on that understanding it is quite certain that most of what we see in the nearby universe still exists and has not changed perceptibly to the naked eye over time spans of several hundreds or even thousands of years (with the exception of things like supernovas, planetary nebulae, etc.)
Finally, back to the proper motion simulator, if you press the M key it will bring up many options that you can adjust to vary the parameters (speed per iteration, etc.) of the simulation.
ETA: If you were to look at the Milky Way from Andromeda, you would indeed see it as it was about 25 million years before you observed it. But that is a very short time relative to the immense time and distance scales of the universe. In the time it takes a photon to travel from the Milky Way and arrive at Andromeda (about 25 million years) the sun will have only advanced about a 10th of the way along its orbit around the Milky Way. And when you looked at the Milky Way from Andromeda, the large scale structure of the galaxy would look quite similar to the way it would look if you could see it "now" even though it is 25 million years older than it was when the photon began it's journey to you.