Due to changes in the way OS X validates code signatures, newly installed Mathematica 10.0.0 and 10.0.1 bundles do not launch on MacOS 10.9.5. This affects only users who install Mathematica after upgrading to OS 10.9.5.
Following are two different methods of resolving the problem:
Bypass the Gatekeeper system in Finder.
a) Control-Click/Right-Click on the app bundle and select open.
b) Wait for the verification dialog to run.
c) Click OK on the next dialog to launch Mathematica.
Bypass the Gatekeeper system in Terminal.
a) Launch Terminal.app.
b) Set directory to the location of the DMG (i.e., cd ~/Downloads)
c) Delete the quarantine attribute by evaluating the following:
xattr -d com.apple.quarantine Mathematica_10.0.1_OSX.dmg
d) Double click on the DMG and install as one normally would.
People who are comfortable with the Terminal (command-line) interface may find that method faster.
Either should be needed just once for that Mathematica.
We will be prioritizing the issue for an upcoming minor release.