If your congregation is consistently disengaged in worship, then you’re probably pretty frustrated. There’s no one single solution because there’s not one single problem. But, if I may, here are three possible ways you might be able tinker with things and see a positive result:
1. Have your pastor on stage at the beginning of the service, to welcome people, but more importantly, to call people to worship
In many, many churches these days, during a worship service, the pastor isn’t visible until he appears on stage to preach. He leaves the opening words of welcome, prayer, and invitation to worship to the worship leader. I think this is a mistake. Whether a pastor likes it or not, he is the primary worship leader of a church. When he doesn’t show any passion for sung worship, people get the message that sung worship isn’t important. The pastor of a church should regularly start the services off with words of welcome and an invitation to worship. And by “invitation to worship” I don’t just mean a nice, safe little sentence that no one disagrees with. I mean really encourage and invite people to exalt and encounter God. Make them a little uncomfortable. The pastor should build expectation and model whole-hearted engagement. When he doesn’t, then good luck to any worship leader who tries to get his congregation to not notice.
2. Videotape your team on a couple Sundays and have them watch it back
There’s a reason why this option feels so unattractive at first glance. It’s because you (and your team) don’t want to know how they look leading worship. Well, news flash: your congregation sees it every. single. Sunday. Here’s the number one thing I notice about vocalists on worship teams: they look like they’re auditioning for a singing competition. For goodness sake, it’s not rocket science. If you’re on stage leading worship, you should be worshipping Jesus. Stop trying so hard to nail “the look”. Just worship Jesus. And here’s the number one thing I notice about instrumentalists: they don’t sing. They look bored to tears. They stare at their music stands. And when they start to sing, they actually seem to stop themselves as if it was an accident and they hadn’t really meant to. Get your vocalists and instrumentalists to watch themselves leading worship. How do they look? Bored? Engaged? Embarrassed? You might need to make some people on your team very uncomfortable so they realize they have room to grow.
3. Give your congregation a year of consistency in repertoire, musicianship, and tenor
Here’s what I mean: your congregation might not be engaged because they’ve become defensive. Why have they become defensive? Because they don’t know from Sunday to Sunday, or even from song to song, what to expect. They don’t want to be jostled to and fro, so they batten down their hatches. Use a repertoire that’s consistent, familiar, includes the best of the old and the best of the new. Don’t try too hard to be clever or inventive. Set a bar for musicianship that’s higher than average, and see to it that you meet it every Sunday. Give people confidence that they’re not going to hear better music while on hold with an airline that they’d hear on Sunday morning. And finally, lead with a consistent tenor from week to week. Don’t be happy clappy one week and Taize the next. Yes, you can have variety in your services. But when people wonder from week to week what in the world they’re getting themselves into, they might just stand and watch as spectators.
Worthily Magnify 
These are really helpful suggestions. Regarding the third point, might this unfortunately work in reverse? To clarify, if a church (like mine) has typically been fairly engaged in sung worship, but has recently begun using three different worship leaders (I’m one of them) with three widely divergent tenors, orders of worship, song choices, and musical standards, is there a danger that people will begin to disengage who were previously engaged?
Related to your first point, praise the Lord that our pastor is probably the most enthusiastic and physically engaged worshiper on Sunday mornings, providing a great example to the rest of us!
I can feel myself actively not wanting to videotape my team and play it back to them, which is probably good evidence that I should. These are really helpful suggestions – thank you.