Symptoms

People Picker control in the Set Delegation dialogue of the OOF settings does not resolve users.
People Picker continuously shows 'working' icon.
 

Diagnoses

To investigate this you may check console view of IE F12 tools IE to identify any possible errors. Another thing to check is underlying SmO which is being used by this control. This dialog/control leverages Get Users method of UMUser smartobject. Verify if this smartobject is working correctly using SmartObjects Services Tester Tool and troubleshoot further based on error you are getting there (if any). You may enable or raise detalization of SmartObjects logging in necessary.
 

Resolution

See Diagnosis section of this KB.