I shadowed a couple of afternoons a week for a while, but when summer classes started, I cut it down to only one day per week. I made sure the doc knew I was in class from 7:30 am -2:00pm 4 days a week. (Org 2 and Organic superlab in 8 weeks!) As far as the observation, yes, I just observed..and it was boring at times and still is...but I made sure I came each time with questions and such so I could interact more with the doc. I know this means alot, because I am progressivly becoming more involved in the daily stuff when I am there shadowing. I also have my EMT license (which means I can legally drive an ambulance! ha!) so, when I am working at the hospital, the nurses let me do vitals, put on oxygen, etc. It's not brain surgery, but people do remember someone who can get in there and do stuff versus someone who just stands back by the wall. With respiratory therapy training, I am able to draw blood gasses in the ER and such. My suggestion would be to get some training in something that you may be able to do while in the doc's office. When he knows you and trusts you...he will be happy to have your help.
So, bottom line, read some things so you can come to the doc with questions..and try to obtain even the smallest knowledge about his specialty. Also, find something that you CAN do and let him know that you are ~certified or whatever~ in this or that and would like to be able to practice your skills if he feels comfortable with that. Also, when I was shadowing an ENT, I about broke my neck trying to look into noses, ears, etc.. After the second patient, the doc got the idea that I just didn't want to stand around and begin letting me look at EVERYthing. Don't be shy when you are shadowing. Doc's can be very intimidating, just be honest about what you want to get out of the experience. Good luck.