Problem in opening downloaded application
Without more information I'll dare another stab in the dark, since the mentioned message comes close to what one sees in the following scenario (see screenshot).
If the application downloaded is not zipped, or packed into a dmg, etc., the executable might not have its executable bit set (or better can lose it).

One can then add the "x" (executable bit) by typing the following in Terminal (found in the 'Utilities' folder) with a space at the end and dragging the executable file onto the Terminal window to fill in the path to it, then hitting 'enter' (right click the application in question, select "Show Contents" and navigate to the folder "MacOS", where the executable lives in):

chmod oga+x 


i.e. "change modification for owner, group and all, adding the executable bit"