The most difficult part of any group or organization is dealing with conflict.
In the case of technical production and worship services, problems typically occur in the very public environment of the worship service.
Here are some tips on dealing with issues that occur during a service:
First, is this really a problem that needs to be addressed?
Live events are well live. No service is always going to go perfectly. So, before confronting someone about a perceived issue, think about whether this was just one of those random things that will eventually happen to everyone, or is it really a recurring issue that needs addressing? Perhaps your tech really had a random problem that was resolved as quickly as their skills allowed them. Praise for fixing the issue may be more appropriate.
Second, a recurring problem isn’t necessarily a personnel issue.
Approach the problem from the angle of wanting to understand what's happening, as opposed to assuming that the problem is caused by a particular person. It could be that the heroic skills of your tech team are preventing the problem from happening a lot more than it otherwise would.
Third, if it is a personnel problem, try to help come up with a solution that preserves the individual.
It's possible that training is needed, and no one in your church has the skills to do that training. Perhaps you can put that person in contact with a tech team at another church nearby that can help. On occasion I learn a lot from visiting other churches and observing or even volunteering with their team.
Sometimes the position is not a good fit any longer, or the job has grown to exceed the person's capabilities. If that's the case then a little pastoral-type counselling may be in order. Possibly the person may already realize this is an issue, but believe that stepping away from that position would be letting the church down.
Give people the freedom and blessing to leave a ministry position, and trust that God will provide a replacement if needed. One fellow volunteer once told me, "If the congregation never sees the hole in a team that needs filling, no one will ever step forward to fill it."
Lastly, never call your tech person out in a public setting.
I’ve been in services where the pastor or worship leader has said something like this to the congregation, "I don't understand why they can't get this problem fixed," (or some such thing making it clear they feel there's some incompetence happening).
If you want your tech team solidly behind you, supporting you to the very best of their ability, then humiliating them in public isn’t the way to solve a problem.
The ministry of putting on a Sunday service is a team effort, and tech people are a part of that team.
An acquaintance who once held a church technical staff position often comments when asked if they’ve worked at a church, "I was a church slave once."
How do you think the individuals on your tech team feel about the experience of serving at your church?