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I was wondering how precise the location of an object in a Lagrange point needs to be to maintain stability, since it seems that several natural objects (asteroids) exists together in some of these locations, and also space missions that have sent spacecraft to them have overlapped in time.

As part of the same question I wonder how close to each other these spacecraft are at this points.

I assume that in real life Lagrange points are not really points (mathematically), but there is a margin to them?

I believe that some of the points are not that stable and require spacecraft to make adjustments. Maybe this control capability also helps them be together at these locations?

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Objects at both L4 and L5 have a bit of an "orbit" around the central point. To simulate this, you'll need to use somewhat complicated rotating reference frame physics. Here is an example of the Jupiter Trojan asteroids. You can see that they all dance around each other in the vicinity of the Jupiter-Sun L4 and L5.

http://youtu.be/yt1qPCiOq-8?t=43s

You could still hypothetically be right at the L4 or L5 point if you had astonishingly accurate surveying equipment to help you find it. I guess people could fight over the invisible point, but it's not of much practical use as far as I can imagine.

The 3 unstable points are a bit different. Although, things will not naturally cluster here in the first place because they are unstable. Any traffic jam which might happen would be completely artificial. That said, if space colonization gets going, it could still happen.

For L1, L2, and L2, there is only one axis along witch movement is unstable and a perturbation grows. Because of that, there shouldn't be a huge premium on the point itself, because you can drift around close to it with a carefully designed trajectory. Everyone doesn't need to live at the same point, but rather a common plane. This is still unlike L4 and L5, where you have some fully 3D flexibility of placement. The JWST already is slated for a Earth-Sun L2 halo orbit, so I think that this basically demonstrates the principle. Avoiding traffic jams wasn't the reason they selected this orbit, but it could be a factor some day.

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