For example, if someone is designing an interface for a product used by doctors for a specific task, the designer will have far less medical knowledge than the doctors using the product. How much will this gap in knowledge affect the design process, and would bringing in doctors (or whoever may be an expert in the field being designed for) to help with the design process to deter this effect? Should the designer research enough to be able to clearly explain what's actually happening when the product is being used, or are they mainly focused on how the doctor interacts with it?
Don't worry you don't need to be a doctor to design a medical interface. However, you should definitely study the domain so you know the context well. You need to interview doctors about their typical process of work and where it could be made more efficient. You need to understand very well the dynamics of the process you are designing so you can account all the different branches of it. The more you understand the domain the better interface you can design.
There is even one advantage when you don't understand the domain well. You can design it well for novice users. In the beginning when you are familiarizing with the domain you start to ask yourself questions. Write them down because novice users will probably ask the same questions.