Our school has a large student base made up of 65% children, 10% teens, and 25% adults. We conduct some classes every day which are dedicated to children, some are dedicated to adults, and we have a family class at 6:30 every evening. That being said, anybody can come to any class.
We have a 65 year old man who occasionally (due to his life schedule) can only attend the 4:00 Children's class. That's OK. Sometimes we have children come to the 8:00 adult class with their parents. Again, that's OK.
There are two issues to discuss here. The first is whether or not it is a good idea to mix the age groups, and the second is how to mix the ages.
You could probably tell that we have no problem with the concept of mixing very divergent age groups together in the same class, training side by side. In fact, we consider it to be a definitive plus. Adults tend to bring a certain focus, attention, structure, and dedication to their training and that can have a very positive effect on the class as a whole. If you've ever taught a class with a couple of attention deficit kids, you'll immediately appreciate the value of adult learners in the room.
Kids tend to have more energy and flexibility and these can be great assets when encouraging the adults to kick a little higher, or do another repetition. I am not (and never would) suggest pitting one group against another (see how high the 11 year old kicks Mr. Miller?), but just the presence of different ages groups causes everyone to 'stretch' a little more.
There is also a great benefit when a parent and child train together. If the parent/child relationship is a positive one, the parent and child/ren feed off each other, they bond, and each excels far faster than if they trained separately.
On the subject of how to conduct a mixed-age class, I can say this - pay attention, remember what kind of class (child, adult, family) was advertised, and make sure that any paired activities (sparring for example) are appropriate for rank, ability, age, and gender. I once saw an 11 year old boy paired up with a 36 year old pregnant women for sparring. In this particular case, the young boy was too scared to approach the baby bump, but even so - bad combination!
Personally, I prefer a class that is filled with dedicated students of any age, but generally kids don't have the personal drive to participate at the same level as adults. In many cases, that is the exact reason the child was enrolled - to foster drive, dedication, and other positive attributes.
So a mixed class is perfect for combining the energy of the younger students with the drive and discipline of the older ones. So long as we use good judgment on pairing (and don't let the wee ones get trompled on), everyone should leave satisfied.