In the mapping editor you have to adjust the faces along the edge of your model. Using planar mapping, the texture is entirely flat... think of it dropping down onto your model and then passing through - still remaining totally flat. If only mapped on the Y axis (top to bottom), then edges which don't line up will stretch like in your screen shot. You can go into the texture mapper and manually move those faces out so they are flat with the rest of the Y axis, or you can try a different type of mapping (box, sphere, shrink map).
MS3D's map editor gives me an urge to hurt things, I reeeally hate it. But hey it's a $25 piece of software so that's forgivable. Try out a few other mapping programs like Lithium UnWrap, or Roadkill, to compare and see what fits best for you. Most of them work with the .OBJ format so you'd have to export your model as that, then edit UV's, then re-import for final export to Freelancer. Sounds tedious, and yeh it is :-/
Alternately you can try out gMax for modelling / mapping. There's a topic here on the forum linking to a plug-in page for it, which gives it export functionality (otherwise it's near useless).
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With MS3D, I found out that I can subdivide groups and map the texture directly onto the surface at the angle from which it's supposed to be viewed.
Once I have it mapped out correctly, I then regroup all the subgroups using the same texture (without "remapping it"). (less entries). The textures show up correctly in game. The mapping coordinates are stored in their respective positions on the texture. (you can look at it and it looks like a mess).
It's a bit more work, but it proved to be a satisfactory workaround inherant in the program.