It's hard to pick just one... Cheese manufacturers would go bankrupt because cheese would now be free. General interest in rope and rope technology would get a significant boost. Conspiracy theorists would claim that the earth and moon have not actually been tied together, it's all a lie. Religious groups would find new and interesting reasons to harass and kill innocent people, especially those who supports the idea of tethering the earth and moon together because various religious texts clearly warn that this heralds the end of times. Several people would try to climb the rope and get themself killed in new and hilarious ways (not limited to fatal rope burns). An unprecedented amount of lawsuits would ensue.
Time flies when you don't know what you're doing