For organizations that have a Chief of Staff to the CFO, what has made that role effective?  What were the primary responsibilities?  Any pitfalls?

It may depend on where the need is the greatest. There are 3 main frames of focus for the Chief of Staff: the leader (their presentations, their communications, their time management / optimization), the Finance leadership team (this is where most probably spend the bulk of time; ensuring this is Team One for members) and, last but definitely not least, the Finance organization at large (training, development, charter/culture, recognition), 

Responsibilities include partnering with the Finance executive team to develop Finance strategy, transformation roadmap and governance; leading strategic projects for Finance and overseeing communication and change management for Finance. Pitfalls - if the Chief of Staff also leads Finance teams/functions, it can be difficult to manage Chief of Staff responsibilities and Finance functions.

Project management skills, strong communications skills, an ability to negotiate effectively between stakeholders, and alignment with the CFO in order to have the authority to move initiatives forward independently.