Enlarge the circle of trust by orders of magnitude and radically accelerate the trust-building process by empowering people to rely on the information even before they trust each other.
Implement a performance review mechanism that allows every employee to give themselves an "A" at the beginning of the period and then summarize what they are going to accomplish to earn that A.
Development of a transparent employment process that results in not only the best person for the position being appointed but also keeps that person by making the company accountable for all promises
In the past 10+ years I have not met a single organisation that does not work with external 3rd parties in some form e.g. cloud service, channel distribution, product dev, legal etc.