How often and in what ways might internal politics factor into project success?

I don't think there will ever be a project in which internal politics do not effect the project. In my experience with projects there is always some personnel or corporate conflict that will put the project on pause or cause the project to get off track. Part of doing a project that requires input from multiple people in multiple people is planning ahead for the unexpected.

You are always going to have some John Doe who doesn't like the plan outline or budgeting of some Mr. Smith and maybe not only because he doesn't agree with the plan itself, it could be that John just has a problem with Mr. Smith himself. How I see internal politics is the pressures that come from those above you, the pressure you have to put on those under you or your peers and the problems that all this working together and agree can bring with it. Maybe someone doesn't have there head in the right place.

(I'll come back to this later to edit and add more)

What is failure?

Failure in my basic understanding is when expectations for any given project or goal is not met. It's when where you want to be falls behind where you want to be. Now that by itself is not necessarily failure. In my opinion failure is when this expectation falls so far behind the goal that it is no longer recoverable, whatever you goal was in no longer obtainable. For example if a NASA rocket has issues and can not launch but it is only a delay to launch again other day I would not define that as failure. Now if the rocket explodes and can never have a chance to launch again then I would define that as failure. So all this is only my definition.

The Oxford English Dictionary defines failure as

 a. A failing to occur, be performed, or be produced; an omitting to perform something due or required; default.

Saying that failure is simply when something doesn't happen as or when its suppose to. Whatever is produced does not fulfill what it is suppose to. What was presented does not fill the need or the needed is not produced at all, it failed to occur.

and then sometimes