First thought... who decides which resources get the glory of working on the sprint team that creates and delivers features and business value each sprint vs. the hazing of working on the support team that fixes the crap. I really hope that if you decide it is necessary to split into these two groups, you at least flip flop the assignment or slowly rotate resources between teams to make it feel like one big team. Otherwise, the supporters will only be mad at the creators and you will fall into the typical us/them developer/QA turf war.
A sub-question was posted on how to handle "critical" issues. It was stated, these are the things that are more important than anything the sprint currently being worked. Several points here:
- If these critical issues are bugs or defects, and they happen often... then it's time to have some courage and discipline and go upstream and ask difficult questions. WHY are these things happening, and HOW can they be reduced in frequency? Instead of adapting to handle them, go to the source and stop them. If you can't because "they" are a different group under different management, then you aren't in an agile organization.
- If they don't happen very often, then this is a simple answer. Let the product owner decide whether the item is more important than items currently in the sprint. If it is, then it should be estimated and should displace a set of stories that are lower priority and of equal cumulative value.
- Work one week sprints. As a support team, you need the ability to be more flexible. Shorter sprints allow for quicker reaction and re-prioritization. Also, work can't stagnate without being noticed. Deployment is quicker (although you might deploy daily and not wait for the sprint end).
- Think about applying Kanban. Loosen the strict requirements of scrum and use Kanban to drive how many things you have in flight at a time. Use iterations as a measurement and assessment tool, and use Kanban to drive priority and work. Walking the board will put the daily focus on priorities.