I found in my jar changes a 1971 s penny, which apparently is a proof coin and I can see doublings on both sides. In obverse, doublings are visible in " IN GOD WE TRUST" and in reverse the "D" in UNITED and "M" in AMERICA are obvious. I like to hear your opinions about this coin, please.
As others have said, it's not a proof coin. Please provide clear closeups of the areas you think are doubled. From the pics you provide I don't see any doubling. The D in UNITED looks like it took a hit.
San Francisco made cents for circulation from 1968 through 1974, nickels from 1968 through 1970, and dimes in 1975 therefore in circulation you will find non-proof coins with an S mintmark.