looks like "float" is not enough for your plane physics. try if "double" solves the problem.
What Krypt0n says: Lack of precision usually manifests this way. When you zoom up close, you magnify this error, and it is seen as jittering, or jumping around. (Anyone hearing 'House of Pain' in their head now?)
Small errors becomes big, and with computers that store finite information (finite precision), you will always have small rounding errors. It is just a matter of finding a tolerable level of error, which may be changing from 'float' to 'double'. If you zoom deep enough, you will end up having trouble even with doubles, but with proper constraints, you can avoid that, like for instance not allowing to go to exactly zero altitude when the ground is at zero. (You don't want to be able to zoom in to see the atoms that the ground is made of...) You have a head attached to your body, for instance, that elevates you a bit from the ground.
Another way to account for rounding errors, is how you define your units, wether you define one meter to be 1 unit, or 100 units, for instance. Bigger values is less prone to be affected like this than smaller values, but bigger values may limit the size of your world, so it is a trade-off.
EDIT: Thinking about it, far too big values may also be a problem, in that it will require a really small value to change the position in a smooth way, so there is probably a 'sweet spot' somewhere in the centre of the two extremes.