This sounds like a recipe for problems to me. As a Chairman, I don't check the draft minutes until after they have been published. As a Clerk, I don't allow the Chairmen to see the draft minutes before publication. All councillors, including the Chair will have the opportunity to correct errors and omissions together in a public forum at the next meeting, but offering them this opportunity individually opens the door for individuals to add or amend items to suit their own recollection or agenda, thereby creating an inaccurate record of the proceedings. If, after consulting everybody, changes have been made, you would need to reconsult everybody regarding the changes, inviting them to amend the amendments. This could go on for sometime!
As Graeme has said, the Chair does not have any executive powers, so rather than allowing everybody else to view the minutes because the Chairman does so, I'd be tempted to withold them from the Chairman.