My boss is consistantly threatening to fire staff. Is there a point where he needs to stop?

so i have a new store manager at a retail store. I am a supervisor and i get along great with managers but he is really pushing my cool. Anyways one thing hes doing is consistantly sying how he will fire us for this and that. The newest of which is for interviewing anywhere else. For example today he said he saw my facebook said i was looking at career positions within my degree like 6months ago and he said he could fire me for that! is this for real? i need my job to pay the bills but id like to pursue my field (i have a college degree). To do that tho i need to interview! anyways can he really fire staff for that? oh and he is not my facebook friend. He somehow is looking at workers facebook pages and always asking ppl about it. He says hel fire ppl for saying anything on facebook to.