Trust is the key
Especially the honesty-related kind of trust, where team members are able to show their weaknesses, are not afraid to be vulnerable and are open with one another. As a result, they will not waste time and energy on defensive behaviors, and are ready to ask for help from each other.
Achieving this level of trust can be challenging, but not impossible. Sharing experiences, following through in multiple ways and demonstrating credibility can definitely help, and so can developing strong insight into the unique characteristics of team members. The role of the leader is to create opportunities where all these can happen, such as in-company meetings, outdoor integration, celebrating special occasions together, etc. And it is worth it, because hiding mistakes and weakness due to the lack of trust can be counterproductive, leading to poor team performance.
One way to develop employee trust is by adopting an open-door policy at work for employees. The purpose is to encourage open communication, feedback, and discussion about any matter of importance to an employee. Employees are free to talk with any manager at any time, including the senior staff, and in this way they pass important information and feedback to managers who, in turn, can utilize the information to make changes in the workplace.
Introducing an open-door policy in a company should be handled carefully, however. There is the danger that it will encourage employees to believe that only the senior leaders have the ability to make decisions and solve problems and, as a result, they will skip their immediate superiors in the process. Taking the matter up with their direct boss first should be made a priority. Otherwise the open-door policy will lead to a communication break-down and will be the first step to kill all teamwork.