identification of purposeful (engineered) genetic changes vs. random mutations
One should be able to tell this from comparison of the sequence with that of the original organism in GenBank etc. The differences in an engineered organism will generally be extensive and of such a kind that a specialist in the field will be able to identify their origin and deduce that they did not arise naturally. 

However there is no general and guaranteed method. If I were to engineer a single base change, there would be no way to distinguish that from a natural mutation. The only thing is that if the mutation were beneficial then it would probably have occurred naturally and I wouldn’t have needed to engineer it.