These "stretch marks" are the pepper equivalent of human stretch marks which form when the muscles & tissues expand at a different rate from the skin covering them (e.g., pregnancy marks or from excessive gym + protein supplements, etc). In this case, the flesh of the pepper fruit expands faster than the outer epidermal layer and the brown spots are from "healing" (the equivalent of our scabs). They are perfectly normal and there is nothing you need to do about it (or can do about it).
I've read from more than one source (and experienced it myself), that peppers with stretch marks tend to be hotter than those without (i.e., smooth skinned ones). This site also says the same:
Ever take home a jalapeño chile pepper from the grocery store and have it either be so lacking in heat it may just as well be a bell pepper, or so hot a speck will create a raging inferno in your mouth? Here's a quick tip for choosing jalapeños that can help you decide which ones to pick. Jalapeño chilies start out mild and progressively get hotter the older they get, eventually turning bright red (and quite hot). As they age, they develop white lines and flecks, like stretch marks running in the direction of the length of the pepper. The smoother the pepper, the younger, and milder it is. The more white lines, the older and hotter. Red jalapeños are the most hot, because they've been maturing the longest.
As far as I understand, this is knowledge derived from empirical observations (as with most of gardening tips), and you will certainly find peppers that are hot and not have marks (e.g., I've never seen stretch marks on habaneros). This might serve as a very rough guideline to pick one that has a higher probability of being spicy from a given set of peppers of the same kind.