When you hire someone, make sure that they're smarter than you are. If they're not, why not just do it all yourself? If you want your company to be the best, you have to hire the best. At the very least, even if they're not smarter than you are, at least make sure they know more about their chosen field than you do. And if you worry that one of those shiny pennies might replace you one day, maybe you'd better get busy polishing your skills.
When you lose an employee - especially for disciplinary or performance reasons - replace them with someone better. If not, your organization will stagnate.
I simply can't say enough about cross-training at every level of your organization. Every company that I have been with that had a cross-training program for new hires had far fewer communication issues than companies that didn't - not least because it puts you on a first name basis with the people in each department, plus their pet peeves and the issues associated with doing their jobs, and the impact that you will have on them on a firsthand basis. It's a lot easier to create a good process if you already know firsthand what bad ones look like from every level of the organization.
When you hire someone, there's typically sag (stagnation & lag) time between their training period and the time that they actually begin to do real work. Why pay someone to sit around and forget everything you've just spent time and money teaching them? The moment training is over, have them sit with everyone who already does the job that they're going to do.
Notice that I said 'everyone' and not 'someone'. This is key. Every person is going to know something different about the job and each performs the job their own way. By having your new hire sit with each person, they can learn all that's good about each team member's process and knowledge, and leave out the poor processes that veteran employees no longer even see.
After your new hire has shadowed every member of their team and taken notes (this shouldn't take long - perhaps 1 to 4 hours per person they sit with, depending upon the complexity of the job), it's time for them to be mentored by each member of the team as they perform the job themselves. Again, the idea is that each member of the team will spot different things that your new hire needs to improve. It's also a terrific way to help employees bond and to create buy-in for the new hire with the other members of the team. (This phase takes longer - likely at least a day with each existing member of the team.)
By the time this training period is over, your employee has the benefit of knowing everything that the other members of the team know, plus a fair bit of practice under their watchful eyes. This also increases buy-in and retention on the part of new hires, who now feel not only part of the team, but also that the company values them enough to put a considerable investment into their on-boarding and success.