In reference to your question, "What is the answer to question 37? What is wrong with mean square error? As long as you are looking at the MSE on the test set... and using it compare models, then I think it is a perfectly fine measure."
The key is, (and the question is not structured in the best way...) the question asks why MSE is bad to compare _models_. It is actually not, used as part of the criteria. But by itself, MSE does not indicate any penalty scoring for the *complexity* of the model. It's trying to get you to say something about methods like the Aikake (AICC or AIC..) modification to the standard MSE cost function, which add a penalty factor for the complexity of the model.