This question was discussed in my class today and I was wondering if anyone could elaborate on this. I was wondering if the Ancient Greeks ran into any problems when they used this method.
Everyone runs into problems with casting. I am not an expert on Ancient Greece but I am a trained metallurgical engineer, so at minimum I can give you a sense of the types of problems they likely faced which may not have made it into many written sources. I can say that, in modern times, the problems faced in lost wax casting specifically are often related to mold filling. Complex shapes are hard to fill completely without some sort of pressure behind the liquid metal. If the process is not carefully managed, the metal will freeze before it reaches the furthest edges of the mold, or it will freeze partially along the wall of the mold and prevent even filling. This can contribute to porosity and other defects. Surface quality in lost wax casting and sand casting is also often an issue, though this is easy enough to polish away.