Last night on halloweens eve a small asteroid flew by at a distance of 0.6 Moon Distances .  
Hereunder an animated gif of the path of 2007US51 (discovered the night before) .  
The picture shows the path of the asteroid as seen from above and from aside , first centered on Earth and then centered on the moon.

The Kozai mechanism for above asteroid is very clear in the picture herunder .
Although eccentricity and inclination vary a lot , the SMA is hardly influenced .
Timescale is almost 50000 years.

Recently a very large asteroid was detected : 2007VA85 , measuring 3.300 meters in diameter . Such discoveries are very rare .  
The asteroid has an inclination of about 132 degrees , meaning it is rotating retrograde to the sun .  
Its path , strongly elongated, brings it beyond Jupiters orbit and inside Earths orbit . The period is about 8 years . I think this is the reason why it wasn't detected sooner . According to the data available now it will never come closer to Earth than 0.15 AU. At this moment it moves away from Earth .  
Hereunder is the result of the simulation of the asteroid for a period of more than 100 years , showing Jupiters influence on the orbital parameters .

It's usually in 3:2 resonance with Jupiter, but sometimes it hiccups as seen from its ~5th to 7th cycle on the graph.  The animation captures the hiccup.  I'm guessing that precession of the nodes is the cause of it skiping a few librations from time to time.

The highest impact possibilty now , apart from Apophis , is given to the asteroid 2007VK184.  
It's size is 140 meter and it's expected to come as close as 0.004 AU to Earth in the year 2032 , thus a couple of years later than Apophis .  
Herunder is an animated gif of the orbit in rotating frame of the asteroid . The orbit is shown in light green. The expected orbit from earlier observations are shown in darker green.  
The latest frames shown the approach of 2007VK184 to Earth ( xy -frame) and the current data from the Neodys site .

Just goes to show how a slight error can become massive over time. Which begs the question to what limit of accuracy can they determine the orbital elements and over the course of the next few orbits how big an error in position does that introduce? To that end how can we ever be really sure these asteroids arent a threat in either the near future or distant future?

I got to thinking about it, perhaps too much but thats just me and the way my mind works. In order to know where something is going to be in the future (time T) we need to know where it is now (time t) and all the forces acting on the body in the time interval t to T. We can't know this as its the future and so we have to guesstimate it. First we have need to know everything about the object itself (position, velocity, dimensions, mass and its distibution, rotation, albedo and probably more) and the same for every object it is going to encounter along the way. That takes care of gravity but what about solar pressure CME's and the Poynting-Robertson effect? Are they significant or over what timescale are they significant? How accurately can we predict any of these? More and more questions seemingly without meaningful answers. Then back to the original question, over the timescale in question how much do these errors compound? The only way to know is to make your best guesstimate and then see at time T how close you were. But by that time it could be too late! Like I said probably thinking about it too much but there you go some food for thought so to speak.

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.