I agree it's pretty scary stuff. However, did you actually watch the whole programme? If so, you will have seen that the majority of the risk is on the West coast. Never say never but I don't think you need to worry too much. There is just as much risk of a hurricane, tornado, freak snow storm, an earthquake, an ash cloud or any other freak of nature. Or a road traffic accident, being run over by a bus or suffering a heart attack (in fact, probably more so).
There have been just 4 reported deaths in Florida from sinkholes - not a high enough statistic for me to be concerned about it