Open Premiere Pro CC 2014 on Mac OS X 10.9, or later. Then, by inspecting the Activity Monitor, you see a warning that says "Adobe QT32 Server Not Responding."
The QT32Server process shows as “Not Responding” in the Activity Monitor in Mac OS X 10.9, or later. This problem occurs because of a bug in Premiere Pro CC 2014. This warning does not affect your computer or your Premiere Pro project adversely, so usually, ignore it.
In Premiere Pro CC 2015, this issue is fixed. You no longer see a warning dialog box in the Activity Monitor. Update the application to Premiere Pro CC 2015 to be rid of the problem.
If QT32 Server is not hung, and a warning dialog box appears, try troubleshooting other possible issues, instead.
There are instances when QT32Server is hung, however.
That problem can happen if QuickTime crashes or gets stuck and never returns control to you. You can determine the issue by looking at the CPU load for that process when doing some QuickTime intensive task (such as, non-native import and export).
This problem can sometimes be fixed by removing faulty QuickTime components from the Library/QuickTime folder. Then, restarting the computer.
Remove older, legacy components first. Allow the QuickTime components still important for current hardware devices to remain in place.
See this blog post by the After Effects team which provides additional information with potential fixes related to this problem with Premiere Pro.