[Suicide Junkie]

You sound pretty pessimistic, Geo...

Given all the people in the world, I'm sure there are enough that are willing to spend the rest of their life on the ship, especially if its big enough to be somewhat comfortable.

At the very least, you could fill it with a load of criminals, as an alternative to death row or life in prison...

-----

As for the mechanicals... if you hollowed out an asteroid, you wouldn't have to worry so much about mechanical problems...
Just keep the power plants running (fusion?), so you have light for your plants and the rest of the ecosystem. Backups, technically trained people, and a small custom parts factory should do it.
You could use Earth power to get boosted on your course, and then the colony needs only to deploy an engine to stop at the end. An ion drive and/or a magnetic sail would be fairly easy to do.
You could even build them just before you arrive, using the latest designs from Earth.

You don't actually need to do anything on the outside of the "ship" until you arrive, except perhaps the occasional telescope observations, and radio/lasered communications with earth.
And the rock will protect you from just about everything.