ASSERTION: "nv > 0" at modelinterp.cpp:4157
This one is impossible to trace, as the code in modelinterp.cpp, which is responsible for interpreting model data and making it usable for OpenGL usage has changed quite a lot from 3.6.12 (which you are using) to 3.6.14 (which is the current RC build). Please run this again with one of the release candidate builds so we can get an error message from that; chances are it's going to be much more usable.
Assert: sip->subsystems[j].model_num == sip->model_num
File: ship.cpp
Line: 14443
As for this error, it's kinda baffling because it's one of those "this should never ever happen" things. The problem here is the following: For each ship, the engine keeps an internal reference for which model is being used. For every subsystem, there is a similar reference (which, while it may sound redundant, is actually a major timesaver in some areas of the code); and since all subsystem models need to be defined in the same model file as the base model, this must be the same model ID. In this case, this assumption has been violated somehow. In order to fix this, it would be preferable if you could post (or PM) the model in question and its associated tbl entry so that a coder can take a closer look at it.