So this box is unusual enough that its effects are best seen not by looking at the box, but how it affects the senses, and how we adapt to them.
The effect on sight is the obvious one. If one cannot see more than a meter away due to the box, the value of sight will diminish. Likely this will lead to nearsightedness, for the same reason books lead to nearsightedness - there's just no particular value in being able to see far anymore.
The effect on hearing is more subtle. You'd be astonished at just how much information our brain processes out of the sound waves reaching our ears. For example, did you know you can tell if something is above or below you, simply by whether you hear the characteristics of echos off your own shoulders?
The box is a horridly designed structure for this sort of advanced auditory processing, so it seems like a likely place to make modifications first. Inside the box, we would start to see custom shaped inserts which give a more organic shape to the inside of the box and get rid of all those horrible boxy echos. Eventually people would get the hang of making them in a way that mimics how the peaks and valleys of the human ear works, giving us a remarkable amount of directional information. I would also expect some clever hijacking of muscles (perhaps the muscles that wiggle the ears) to control the size and focus of the opening. Wiggle your ears up, and the inserts may open up to let you hear smaller sounds better!
The sense of touch would become far more important, because each person's world would get smaller. The things that matter in the world would always be close into you. If a friend was across the road, you might not even know it unless you recognized their footfalls!
The single most monumental change would be the inability to see someone's face as you talk to them. The amount of emotional information conveyed in the face is staggering. Society, however, is not one to give up the good fight. We would develop new ways to convey that emotional bond. Touch is a powerful medium, so we may see it become proper etiquette to touch hands while talking to someone. Kissing the Papal ring is a ritual in our age, but that opportunity to touch the papal hand would actually be incredibly meaningful in this society.
Of course, talking would be less popular. With the inability to see who can evesdrop, broadcasting communications like that are risky. Every individual would know some sort of sign language which can be used between two people (or perhaps even more). This would double as an excellent way to convey emotions with the hands.
Now for the list:
Dating
We would find ways to be "shallow." The ability to show beauty at the skin depth will not be lost simply because we don't have eyes. Careful care of hands would replace careful care of the face. Physical contact would be a lot more important in dating. Whether that makes dating deeper or more shallow is really up to you.
Sports
Sports would consist mostly of tasks which could be observed by touch or very short range sight. I would expect strength games like tug of war would be very popular. I would expect not to see very much in the way of speed games. A lack of visual capability means its much more dangerous to go quickly, so it won't be valued as high.
Entertainment
Group entertainment would have to be auditory, so singing would be a major form of entertainment. People would also likely dance, given the tactile feedback one gets from dance. Obviously there would not be anything like movies.
One thing which would have interesting changes is magic. I'd expect close-quarters magic to be a major pastime because it is almost perfectly selected for by boxing everyone's head.
Crime
Your instinct was that crime would go down. However, I disagree. I think crime would skyrocket. One of the primary tools our society has in place to deal with crime is the justice system. Justice depends on identification, and the box removes virtually all methods of reliable identification. Heightened hearing might help, but I would expect drive by muggings to be a major problem with little to no response possible.
The only solution would be for your dictator to have an iron fist rule. But then crime isn't decreased by the box, its decreased by the dictator
