I am not sure if this has been reported, but LODs of animated objects are not synchronized with each other. It means, that when switching from one LOD to another, the animation is usually started from the beginning which makes the object "jump" to a different position. Some simple objects can be done with no LODs however more complex - can't. Would it be possible to fix this in the future?
Here is an example. The plane in the middle is animated. High LOD:
Switches to low LOD and instantly changes position to the beginning of the animation: