This is a very large question, much larger than just scrum. It reaches to the core of team play. The idea of giving more control to the individuals is to make them more efficient by removing red tape. However, there is a tradeoff. With red tape in the way, everyone is marching towards the same goal inefficiently. Take the red tape away, and everyone marches efficiently, but towards their own goal. If you have instilled a good sense of the overall project's goal in all of the individuals, this works great. If the individuals disagree on the final direction, then bickering begins.
I recommend two techniques beyond the obvious "unify your team goals a bit more": one is to give remove the red tape slowly. Give the team time to react to the changes, and see if they can re-align themselves. Sudden changes in development rules are much harder to get used to than the gradual ones. The second is to attack the problem from a higher vantage point. See if you can have a meta-control on the problem such as, "if I see bickering, the red tape comes back until we all calm down."
The last bit of advice I have is to never approach two team-members that are butting heads directly. By definition, they are in butting heads mode, and they won't mind butting heads with you as you try to fix things. Always seek to move them out of opposition, rather than trying to manually squelsh the opposition directly by making a decision for them.