A really interesting question Dan. For me:
1. Ability to attract and inspire quality assistant coaches: I think this is critical to the success of any senior manager, but especially here. A national head coach shouldn't need to focus on the day to day coaching of the national squad, in terms of drills, workouts, implementation of game strategies - he/she should be able to leave that work to top-quality assistants. The best creative ideas will probably come from younger assistants and the players, so a head coach should create an environment that attracts the best assistants and challenges them to become better - the head coach is a coach of the coaches.
2. Fit with the rugby environment: Some head coaches will step into an environment that provides lots of existing support, in terms of recruitment, pathways, established style of play, etc. Some head coaches will have none of that. Different situations require different skills and strengths. A successful coach in the well-supported environment may be someone who can manage the people well (see point 1) and "bring people along", focusing on incremental change and improvement. The coach with no support may need to be someone who is ruthless and demanding, bringing order where there is none. For better or worse, I think Cheika was the right man for the Tahs and the Wallabies at a time when there wasn't much vision or adequate structures. He didn't thrive when those structures started to be built around him.
3. International experience: The national head coach role is so different to a club head coach - there are so many layers below a national head coach that he/she must work through (clubs, juniors, national pathways, overseas players, etc). This is my only concern regarding Rennie, his lack of national experience. However, good support (see point 2) could minimise the risk here, sharing the workload.
4. Rugby knowledge: Yes, needed. I don't buy into the idea that a successful coach from another sport or corporate life could be a successful national coach. However, it is interesting how many successful coaches at provincial or national level have experience outside of rugby - school teaching, business, etc.