I am having nightmares about this, since every time I tried to do any kind of brisk walking in the past, I ended up stopping because of the dreaded shin splint.
Here's some advice from an old distance runner on how to prevent shin splints. Most of the muscles in the human body are arranged in opposing pairs (think biceps/triceps). Problems can occur when one set of the opposing pair becomes much stronger than the other, creating an imbalance. Shin splints are caused when the muscles which push off when you step become much stronger than the muscles which pull up. You can prevent shin spints by sitting on an elevated surface (I used to use an old, sturdy, metal kitchen table which had been relegated to the basement), hanging a bucket filled with a light barbell or dumbell plate (say 2.5 lbs or 5 lbs) from the tip of your toes, and doing repeats of lifting the weight up, pivoting at your ankle. In other words, you are doing the opposite of the pushing-off motion you do thousands of times as you run or walk during your daily exercise regimen.
I've been very fortunate in my bicycling in that I have largely avoided any sort of knee problems. When I first started cycling last year, my saddle was slightly too far back. Most of the time, I found myself almost unconsciously scooting forward just a little to compensate--this prevented knee problems but caused some saddle soreness. When I consciously kept my sit bones positioned over the proper part of the saddle, I sometimes started have very minor pain in my knees. So, I started adjusting my saddle forward in
very small increments until I solved both issues.
Gee--there are so many ways in which one's fit may be off which could cause knee problems. Your saddle may be too high, it may be too low, it may be too far forward, it may be too far back. Are you using clipless pedals? If so, maybe the toe-in/toe-out angle needs adjusting.
If you have a lot of patience, you can solve this on your own by making one small adjustment at a time, riding on it for a while, and seeing if the problem improves. If you want to speed up the process, take your bike back to the shop where you bought it and describe the problem to them. Finally, you may want to consider getting a professional "bike fitting".