Sometimes when walking across the fields, woods, and hills, you're going to run into obstacles. If you have children, older folks, or simply greenhorns, you must never assume that people will use common sense to traverse a rough area. People are NOT used to taking any trail, much less crossing though a forested region without a trail or uneven ground.
If it's possible, have an experienced person in the front and the back. The person in the front is noting all of the things that might be issues like low lying branches at face level that can hurt your eyes when bending back and forth, rocks that people could trip on if they are clipping along, holes where they could twist an ankle, etc. That person tells the person immediately behind them, and so on. Teens can really help here, and can be taught so well, that they might see the obstacle before you do.
The person in the back is making sure people are not straggling which will greatly diminish your speed. If being quiet is an issue, they're reminding them. They're also observing who is behind them, and noises they hear.
Crossing water is always an issue. It is very easy for someone to be foolish or play, and a twisted ankle or injury could become a disaster. You need to show them how to cross, and in the most practical way. Having a large branch or staff to help balance themselves will really help. Swift moving water can knock someone off their feet, and often mud can make people lose their shoes or get into a dangerous predicament. Wet mossy rocks are horribly slippery, and no doubt someone will take a spill.
If you lose your footing in a river crossing, and get carried downstream, lift your feet up in front of you always. Teach them to move parallel with the river bank, and inch towards it, rather than make a swim directly across. It would seem that swimming right for it would be smarter, but not in fast moving water.
Going up a hill, lean into the hill. Be cautious about grabbing on to branches. I've seen people do this, and fall a great ways with a nasty scrap. A staff can often be used if the soil is lose to plant it a little, giving you far more steadiness as you ascend.
When going downhill, if it's too steep, go down on your butt. Inch along until the terrain doesn't have loose rock and flattens out some.
Sometimes you have to traverse a rocky cliff. If so, lean into the rock and look straight across. There are often lips and handholds. I've taught 7 year olds to rock climb. Sometime they pay attention better than adults. It is extremely hard to rock climb with a novice child. Try to have them practice in an area that is not too high at first so you can watch their technique. Teach them to use their thigh muscles, not relying upon upper body strength that much.
Chimneying is a technique where you press your back against a crevice and then press with your feet on the opposite side. You inch your way up or down when there are no hand holds and you must go either direction. Anyone can do this as strength needed is not as important as the crevice opening. It's like kids do in doorways to inch up the door opening and ascend to the top. That's a great way to teach children.
Any crack that potentially could be a great handhold in a public park could have glass in it. There's always some nutty person who might have thrown a bottle. Teach people about this. More than once, I've reached into a crevice for a critical handhold, and gotten cut by broken glass, and still had to hold on. I've never gotten cut when I watched for it and paid attention.
If someone freaks out on a cliff due to fear of heights, talks to them calmly. Everyone has the potential to get a bout of anxiety. Have them look immediately ahead, and not down. They can tense up, building lactic acid in their muscles, and it can go horribly wrong. Watch for trembling if they stand in one spot too long. Better to walk ten miles out of your way, then lose them.
Older folks can lose feeling in their feet. It's called neuropathy and affects many people. It can be the reason they lose their footing since they cannot tell when their feet are touching the ground very well. You must watch out for this as they will be embarrassed and not reveal this.
In any ascent, it can be very helpful for the experienced person to go right behind anyone you think will give you trouble. Sometimes the strongest person who's full of bluff and bluster will not listen at all. Watch for this.
Better to take your time and guide every single person through a tough place to navigate, then an injury that could lose you days in hiking.