Looking at the pictures I am perplexed how the screw holes on the PSU don't align with the case. Looking at images of the back of the case and the PSU both have standard ATX positions. I don't want to doubt you but have you got the PSU the correct way up, the holes are positioned so a PSU will only fit one way up in the case.
To be as safe as possible really you just don't want the PSU dangling by cables (so the cable is taking the weight), you don't want the PSU laying so its fan outlets are blocked and I would put the case somewhere you won't trip over the PSU or kick something into the case.
Oh, and don't leave it lying so it's easy for the contents of your desk to fall straight into the open side.