What are the "blind spots" of the Ebers-Moll bipolar junction transistor model?
The EM model is a very simple and limited model. If it covered everything there would be no place for NXP's Mextram model, the Gummel-Poon model or the Hicum model.

As a circuit designer you must always be aware that a model is just a model. A model is just a simplified version of reality. So you can never trust a model 100%. How much you can trust a model depends on how you're using the transistor, under what conditions the model parameters have been derived and many other factors.

It is typical for beginner designers to either trust the model 100% or to worry about model accuracy so much that they don't dare to trust anything. It takes experience to judge these things properly.

The trick is to make your circuit designs such that the actual properties of the transistor are less relevant. For example, say I do not trust the Early voltage prediction of the model. Then I would try to use a cascode so that the Early voltage does not matter much anymore.

Oh and a final note: For BJTs in general modeling is quite good. For MOSFETs there are far more issues regarding modeling. Yet still we can make working circuits :-)