You're going to love these links. This is Jon Giorgini's paper on predicting the Earth encounters of Apophis.
http://neo.jpl.nasa.gov/apophis/Apophis_CORRECTED_PREPRINT.pdf In the paper he discusses the difficulties in predicting the circumstances of Apophis' 2036 encounter with Earth. Factors include:
Perturbations from other asteroids that can shift its position by several Earth Radii by 2036.
The Yarkovsky effect, which we can't predict without knowing the details of its rotation and albedo, can have an effect of several Earth Radii
We don't know precisely where the planets are. Uncertainties in the positions of the planets themselves can cause an effect of several Earth Radii.
If you don't want to read the whole paper, here's a short article that summarizes the paper:
http://neo.jpl.nasa.gov/apophis/ If anyone is interested, I can make some new Apophis simulations, one with additional asteroids, and one without, so you can compare the difference yourself.