The devil is in the details…… What does this mean. The basic definition is that the small details are really important. Without them whatever you are working on may fall apart. This is so very, very true in the Martial Sciences. When training pay attention to the technique you are working on and highlight in your mind the small details of why it works. Listen to whom ever is showing you the technique and ask questions regarding all aspects of it if needed. That way you will be able to replicate them again and again. The small details in the Martial Sciences are essential if you wish to be successful in them or a violent confrontation. During the course of your training always pay attention to the small things. I cannot tell you how many people I have taught that came with previous training who were missing small details in their training. A lot of this I attribute to large class sizes but also to instruction and their own inability to focus in on the details during training. I have had people come to me claiming extensive grappling experience yet they miss way to many of the small details for it not to be understood that they actually had very little training or really crappy training. You see if you do not know the details someone else will. Someone else you may be training with or worse someone could exploit your lack of attention or knowledge of the details in a violent encounter. So in your training look carefully and listen carefully and see the details, understand that they are really, really important. Train with them in mind and you just may see your ability increase exponentially!
The Instinctive Edge™ 
One of my pet peeves here is when the teacher says “Watch me” that some people try and copy the teachers movements, at that moment, when they should be watching or they take that as time to socialize since they are only supposed to be watching so it does not require their full attention.
Like you said, “the Devil is in the Details” and it is at those moments, when your teacher asks you “watch” you can start to see those details
Absolutely Tim, some times just watching allows you to see the little details!
A teacher I personally know was injured for quite some time. During that period he still went to class and just watched or video recorded for his instructor when asked. He told me so many times that this period was a fundamental growth period for him because he really paid attention to the little details. It made all the difference in the world for him!
injury can be a great teacher, maybe not the preferred one, but it can be a good one