Engineer, Technical Advisor, Artistic Advisor, Manager, Friend, Councillor... The producer must be all this and more. The actual role of the producer is very hard to pin down however their responsibility is to do anything they can to make sure that the artist works well and ends up with a great sounding record. One thing that is for certain is that the producer should have proven experience in making good records.
The producer and the engineer can be the one and the same or they can be individual people, either way it is important to designate a person or persons to the task and entrust them with the control of the direction and sound of the music. Having just one or two people that you can trust to make decisions will result in increased productivity and less arguments. This is not to say that no one else can have any input on the progress, rather the producer will listen to the input of each person and make an informed and experienced decision that they believe will give the most benefit.
The producer has many things to think about during the production of a record. They have to think about which songs should be recorded, the order they should run in, the length of the songs, the instrumentation, the arrangement, the musical direction, the technical aspects of the process, the lyrics, the performance... The list is endless. It goes without saying that the producer should have nothing else on their mind than the quality and progression of the current work.