Recently I had to upgrade my power supply, and I find it won't fit into my case. Rather than going out to get another one, I simply plugged it in on the outside of the case and left the cover off. Is this safe?
For a sturdier solution, drill/saw/chew a hole in the computer case to let the PSU cables through. Then put the cover back on and tape/glue/screw the PSU on top.
I run both of my machines with covers off, no problems. Have done so for many years. But as Nodsu said I would try to get that PSU tied down to something.