It could be that you are just preoccupied and that your mind is elsewhere. Staring at others can make some people feel uncomfortable whether there is intent there or not.
I'm not a very social person and when I was younger I would observe people. I guess this helped provide information on how best I could fit in, I'm not sure. Maybe it is a way to participate without actually participating or engaging??
I too would obsess over stuff. For me it was about trying to be perfect. I'm not sure if this is what you are experiencing.
Me too with being late and for me that is due to ocd. I get stressed and anxious and repeat stuff for long periods. I then find myself panicking because I am late.
A good place to start could be with your doctor. Understanding what is going on will help you to treat the problem more effectively.
The expert on the compulsive behaviors expert forum had a site he would recommend for those with ocd. You might like to visit some of the archived posts there.
The boredom variable in my opinion could be a valuable clue. I'm not sure if something like ADD could apply. Talk to a doctor and get properly assessed and take it from there.
Good luck.
I agree with Jaquta that there are a number of possible explanations... Attention Deficit Disorder is associated with an inability to stay normally focused (all of us drift off a bit when we are bored). Then there are a number of anxiety conditions that could be distracting you because you are preoccupied with worries when you should be staying focused. I would try to keep track of when you are distracted. Cognitive Behavioral Therapy (CBT) begins with monitoring yourself, so that is a first step. Find a way of writing down the date and time of these events, and ask yourself what you were thinking of... see if there is a pattern.