That is the same problem as here:
Dyld Error Message:
Library not loaded: /Library/Frameworks/PluginManager.framework/Versions/B/PluginManager
Referenced from: /Applications/Aperture.app/Contents/MacOS/Aperture
Reason: image not found
There is a dynamic library missing from you system library.
The easiest way to fix this is by reinstalling MacOS X. Boot into recovery and reinstall the system. You can install on top of your current system, see: OS X: About OS X Recovery http://support.apple.com/kb/HT4718
This error is usually cause by an old installation of Final Cut. Did you recently install Final Cut?
See: Aperture 3.x: Aperture unexpectedly quits if Final Cut Express 4 is installed http://support.apple.com/kb/TS3528
I sure hope, the recent Mac OS X update 10.9.3 did not bring this old error back.