On Mac OS X, when I run Firefox (and Thunderbird, and ...) which I downloaded from Mozilla, the OS pops up a warning that the file was downloaded over the internet, giving the date on which it was downloaded. I have no problem with that warning on the first time I use a downloaded application - but the repeated warnings are a nuisance.

Is there a way to suppress that dialogue box?

Is there a way to avoid it appearing in the first place? (Some applications I download from a corporate intranet - those don't produce the equivalent warning; any idea what the criteria are for when the warning is generated?)