Good question about the precision; we only hear little snippets about hitting virtual windows in space within 100km or so. New Horizons is running a MIPS-1 R3000 processor[0], that has double-precision floating point available but presumably fixed-point arithmetic could be more suitable here. But I don't know that there would be so much accumulated error, there were a few course corrections between Earth and Pluto. Maybe the precision is not so much of an issue?

As for the fly-by, well. Speed is a problem. At the point of closest approach to Pluto it was going at 13.78 km/s, and it's about the mass of a grand piano[1] so that's about 45TJ of kinetic energy. Or some large number anyway. Let's just carry on with Newtonian stuff and assume the numbers get worse if you do it properly. At current speed its orbital radius[2] would be about ... 4600 metres. Three miles!

That's somewhere deep within the icy core, I'm guessing.

In order to orbit at the distance of the photos we're getting now, it would need to slow right down to 264m/s, shedding basically all of that kinetic energy. Back of the envelope numbers suggest that would require about the equivalent of a 90 megaton explosion! Of course, if we strapped the Tsar Bomba[3] onto New Horizons, there would be more mass, so we'd need more stopping power ... and so on.

Other reasons for doing a flyby, I suspect, is that we get to see more stuff this way. There are a few moons, and an uncharted Kuiper Belt. Seems a shame to come all this way and only see the one thing. Not to mention the allure of the tantalising glimpse ... always leave them wanting more! This mission started with Pluto being nothing but a blurry dot occupying a dozen pixels. Imagine what the next mission can do, based on what we're already learning! Iterate and improve.

[0] http://blog.imgtec.com/mips-processors/mips-goes-to-pluto [1] https://what-if.xkcd.com/137/ [2] http://www.physicsclassroom.com/class/circles/Lesson-4/Mathe... [3] http://nuclearweaponarchive.org/Russia/TsarBomba.html