Although the producer is primarily the one who makes the "recording decisions" - vs. the engineer who primarily "gets the sounds to tape", there are so many other things a producer often does.
A producer may also act as an arranger (or hire an arranger). The producer often hires the studio talant or hires a "contractor" (the contractor is a studio musician who hires all the other session players). The producer has to deal with the record people - and in many cases may also have to make the decisions and arrangements for mastering and sometimes duplication.
Although I understand that this site is about "home recording" and the kind of big budget producer I have described may not apply - I have found that in my humble little studio, I often have people come to me with no clue as to how to convert thier song ideas into a finished product.
I've had to learn how to re-write, arrange, contract, communicate with mastering engineers and duplicating houses and dozens of other small but significant functions. Since I can play several instruments I've had to add/fix performances (oh yeah, I forgot I have to engineer too). I truly belive that in some cases if I didn't know how to do all these things, I'd rarely get past the one-off demo.
I do agree it is very important to establish these roles at the beginning of a project and comply with your assigned role, but I must admit there have been times where I've been limited to the role of engineer and I have to really bite my lip when various recording decisions are made. In particular, it drives me insane when vocals are flat or instruments are out of tune (or just sound like crap) and no one seems to notice, or care.
