I was just playing through the Ark again and got to the cutscene where you activate the silent cartographer. A galaxy comes up, and It's spiral, just like all the scientists at NASA, etc, envision ours to be.
And yet when you look up in the sky at any time earlier during that level, the galaxy theat you see is of an entirely different type than the one shown in the silent cartographer cutscene.

Continuity error? Or are we even further out than we thought?

I'm ascribing it to atmospheric as well as spacial distortion considering the distance between the Ark and the galaxy. Both are the same galaxy (aka the Milky Way) as confirmed by Frankie. As for an official explanation, Bungie hasn't given one.

In Halo 2 level Delta Halo ,as far as I can remember, when you reach the site where you have to activate a bridge to pass to the other side(where a couple of wraiths is waiting) with a scorpion, enter the building where the switch of the bridge is located. If you look on the floor you will notice it is made of glass. Some where in the room there is some sort of a hole. If you go through it you will get directly underneath the glass floor. There you can hear a Prophet speaking of the great journey. Now if you look UP you will see that on the glass roof (the floor of the upper room) is projected a holograph of a galaxy!!! The galaxy is unnoticeable from the upper side of the glass floor since there is a hologram of a Prophet surrounded by some Elite, Jackal and Grunt guards.

Go find it and tell me what you think. Is it the Milky Way? I haven't seen any posts about this galaxy anywhere around the web so I cannot upload an image. So you will have to find it by yourself. Level Delta Halo, Room containing the bridge switch, go under the floor by a secret corridor inside the room, look UP and see the magnificent hologram of a galaxy...

You may be seeing a difference because we are so far away from the galaxy. Light only travels so fast. We may be seeing our galaxy as it was hundreds or thousands of years ago.

But then how far out are we? How fast is slipspace travel, anyways? And how long did it take the crew to get there?