Is jMonkeyEngine considered good for 3D mesh manipulation and analysis?

Operations like aligning 3D objects correctly (according to some definition of correct), calculating difference between two similar meshes, illustrating these differences, etc.?

And is there a good community of freelancers, that could perhaps implement something like that? (Where could such freelancers be found - here?).

Not so much CAD functionality, but more like analysis. The ultimate end goal is determining how well a mesh fits with another corresponding mesh, and what the deviances are like.

Precision does not have to be very great. The mesh would typically be in a bounding box of 50 x 30 x 15 cm. Precision should be something like milimeter-scale.

So You don’t need 3d engine, You just need good math package that will calculate everything for You.
Either You should try MatLab/Octave (with some visualization) or Python + SciPy (zero visualization but far better language to deal with).

Then MatLab and Octave it is (both have awesome visualization and they are designed to make such geometric calculations). Using jMonkey for that would be like having all visualization in the world without actually having data to visualize.

Yeah, it looks like you’re more after the measurements which is not a usual concern of a game engine. JMonkeyEngine can visualize pretty things, but you would have to think about measurements yourself - it is a completely orthogonal concept. You could write the maths yourself or use some Java library. Other than that, as others say, you could go with some scientific package made specifically for what you need (they don’t usually provide great means for visualization though, just some bare minimum).