The CPU doesn't have pins, the motherboard does. You'd need to look at it carefully, possibly with a magnifying glass, and see if you can spot any pins that look bent or broken. Do you have any reason to think that there are broken pins?
What happens if you touch the top of the heatspreader? Nothing really. I guess the oils of your skin could interfere with paste application/heat transfer a bit, always best to a have the surface as clean as possible before applying paste.