I agree with Fish Styx. I've had diseases and pests and algae takeovers and a slow leak last year that at least gave me time to move the livestock and drain the tank....but a catastrophic blowout or a house fire are what make me sweat.
Oh, I guess I also worry about floor failure. My tank is oriented parallel to the floor joists, so before installation I went down there with foundation blocks, 2x8s, and jacks. I put up a header supporting about the midline where the tank sits. But since I've had water issues in the crawlspace, I do worry about those blocks shifting and the floor supports not working right, leading to a busted floor. Had a guy down there about a year ago doing mold remediation and I asked him if he noticed any issues with the header/jacks and he said no, but I still worry!