I wish I could up vote this twice. Assume every step in the process will fail and have contingencies. Don't set yourself unrealistic timelines, this will create pressure on you which will lead to more mistakes.
After a while we noticed a pattern. Whoever 'blinked' first got a bunch of theatrics, including claiming a week for week slip every time (even if the problem was only one feature they barely used). Eventually half the teams would also claim a week slip. Anyone who missed that second deadline, the same process would repeat. Some teams who weren't 'the bottleneck' were still writing code week three.
Eventually we figured out that when we said a week, we meant 5-6 business days. When everyone else said a week, they meant 8-15 business days, and we suspected corner cutting even in those numbers. Over time we started 'helping out' people at the interfaces, slowly taking over ownership of more and more surface area. And yet these other teams still struggled to ship on time.
By the end I realized that this was the organizational principle the company was built on. Take a 2d plane of responsibilities, distribute people randomly on the plane, and where one fails to thrive, its neighbors grow to fill the space. You ship when most of the map is covered, and the gaps represent emergencies and/or lawsuits.