In my opinion, the best way to build team accountability is through establishing a culture of engagement and accountability in the project environment. This requires well-constructed project governance.
Project governance describes clearly the roles and responsibilities of each team member in the project to avoid the blame game. Project governance should be tested to make sure it serves the purpose. When putting the governance together, the design should consider the project environment, team size, organizational culture, and ethics. The project governance should encourage team engagement, communication, and self-management. Team engagement in every step of the project is a key component of the planning and decision-making effort. For example, when the team is engaged in the task estimation effort, they tend to be more committed to perform within their estimation and complete the required work for every deliverable accordingly.
The assigned tasks must be challenging not in terms of the time required to complete the work but challenging to the team's knowledge and talents as well. Open and frequent communication can help teammates understanding the complete picture of the project and not just the assigned tasks and educating them about the inter-dependencies of the different activities is as important as understanding the assigned tasks. Finally, building team accountability is building a system that is based on fairness so the team can feel that justice is served.