1st. There are no safe martial arts environments. It's a martial arts school. Depending on your clients toddlers vs adults the most that you can hope for is managed injuries. By this I mean that students will get injuries, like bruises, scrapes, scratches, sprains, and strains. These are the injuries that you will need to manage. The other type of injuries are more serious, concussions, dehydration, breaks, eye pokes, dislocations, and the sort.
The types of and frequency of injuries that are likely to occur will vary with each Martial Art system, so you would need to be more specific in the type of school you are referring. A Tai Chi class for seniors does not have the same risks as a BJJ school or a martial arts class for toddlers.
Monitoring serious problem will also depend on you clients. Teaching children requires more of an active monitoring than adults in their 20's - 40's. Senior citizens, students with health issues, may need more active monitoring for different reasons not related to martial arts, but related to strenuous exercise.
These are just some of the things that students can do to themselves. It doesn't begin to touch on injuries caused by instructors. Soft playful punches from someone who has been training hard for many years will still hurt a beginner student who is not conditioned. This is especially true with children and women.
I personally don't think there is an "automatic" monitoring solution unless you can be specific on what you want to monitor.