If a team is consistently ignoring the issues posted by another and causing issues in the overall project, that's up to higher management to resolve and reprioritize things. Higher-management needs to collaborate and prioritize issues across teams, as their "own" team, since they should have a higher level overview of the project.
To make it a bit more concrete, lets say you have 10 teams of 10 people, each managed by a manager. Each of those teams is an independent "project". The 10 managers themselves form a team that has to ensure those independent projects form a coherent whole by organizing amongst themselves and prioritizing tasks across teams accordingly.
EDIT: this split can work (albeit poorly) at up to 3 levels deep, so ~1000 employees total on a "big project". If you can't make do with that many, you're screwing up somewhere, but 100 should be enough IMO.