I am having the same issue - in the first training mission, the Myrmidon model doesn't load properly. I can see the internal cockpit textures, and the engine glow, but the rest of the ship is invisible.
I ran a file integrity verification, it found an error and re-downloaded some stuff but this did not fix the issue.
So I ran the fast debug and upon clicking the Ready Room door on the main menu, I got the following information:
"Warning: Couldn't open texture 'myrmidonuv'
referenced by model 'Myrmidon.pof'
Edit: I tried again after turning off shadows as suggested in the previous reply, unfortunately this did not work.