I also understand that orbits can be calculated precisely, however there is always a margin for error when it comes to passing objects. We can't accurately predict how other gravitational forces will affect the object, including this present passing.
Of course we can. We can calculate the gravitational influence of any known body; it's just math. If it weren't possible to do that, we'd never have been able to send space probes on courses so precisely calculated that they could reach an exact rendezvous point years after launch and astronomical units away from Earth. That's precision tantamount to threading the eye of a needle from a continent away.
The only uncertainties come from unknown objects whose gravity could influence its course, but we've identified most of the large near-Earth asteroids by now, so there's not that much we don't know about objects that might affect 2012 DA14's orbit -- which is why the margin of error is on the order of one in five million. And of course it's not like we're going to forget it's there. Assuming civilization doesn't fall from some other cause in the interim, we're naturally going to keep tracking it, so if something does change its course, we'll know about it.
They may be able to predict if it will bend it in such a way as to bring it closer or further away on the next pass, but I don't believe they can make an accurate estimate on the exact distance it will pass next time.
Yes, they can, within an accuracy of plus or minus about 20,000 kilometers. Heck, NASA's already done calculations for not just the next pass, but
the next 25 passes going up to 2137, and you can see for yourself how detailed the calculations are. This is the only pass prior to 2087 when it has any prospect of coming closer to Earth than a hundredth of an AU (1.5 million kilometers).
Even this time, there was open speculation on whether or not a satellite might be damaged since it passed inside the ring of geosynchronous weather and communications satellites. If measurements were truly precise, they would have been confident to say there was no possibility of a satellite being damaged.
That's not a meaningful comparison. Precision is a matter of scale. Sure, we can't estimate its trajectory down to the meter and know if it'll hit a satellite or not, but the Earth is over 12,000 kilometers in diameter, so thousand-kilometer precision is more than enough to be sure it won't hit the planet.
Besides, if you look at the table above, there is no point in the next century where Earth's position will even be within the margin of error in the calculations, even the ones with the largest uncertainty. Yes, there is always a margin of error in orbital calculations, a cone of possible paths an object might take from its current observed position. But it doesn't matter how wide that cone is if it never intersects Earth's path. This is why you so often hear reports that some asteroid might potentially hit Earth get quickly followed up with, "no, it won't hit after all." It's because initially the margin of error in the object's course is wide enough that the Earth's position at the point of intersection is within the cone of probabilities; but as further observation refines our estimate of the object's course, the cone narrows and no longer overlaps Earth's position. As long as the cone doesn't intersect Earth, it doesn't matter how precise it is beyond that; whether it's got a 1-kilometer or a 100,000-kilometer margin of error is irrelevant if the minimum possible distance it would pass by Earth is 500,000 kilometers. Either way, the probability of an impact is zero.
Relatively speaking, for a passing object to fly within the ring of geosynchronous satellites is EXTREMELY CLOSE compared to the orbit of the moon. I wonder how much advance warning we'll have with a larger object, say of 3x the size. Something like that could cause a massive disruption to our environment and extensive damage to life and property if it landed in a densely populated area.
As you can see from the link, as long as we're aware of an object, we can have over a century of advance warning. We do track these things. They don't disappear and get forgotten. Once we find them, we know where they are, we can compute where they're going, and we keep them under observation. The only objects you need to worry about getting caught off guard by are the ones we
haven't discovered yet, like the one that blew up over Russia. And hopefully that event will prompt governments to improve funding for skywatch programs so we can find the rest of the significant objects out there and track them too.
EDIT:
Here's an article with more information about the Russian event and the effort to identify and track near-Earth objects, as well as an explanation of what caused the explosion.
