Hi Hans,
The idea that it works differently between Project 2003 and Project 2010 is not that surprising. There was a signficant re-write of the scheduling engine with Project 2010 to allow manually scheduled tasks.

I don't believe Microsoft supplies helpdesk type answers. You are certainly welcome to post your question to other forums or to see if others have more ideas.

I am not a giant fan of Must Finish On Constraints because they lead you to believe everything is okay - the task doesn't move. I'd look for tasks with negative Total Slack - those are the tasks that are in trouble (similar to the Planning Wizard warning).