Large ping times in normal mode, okay ping times in safe mode I pinged google.com to see that ping times ranged from 54 ms to over 2000 ms on my MBA. After a quick isolation and testing, I figured that it was my MBA only issue. I log into safe mode on my MBA with Mountain Lion and I suddenly get ping times of around 15 to 30 ms, which I think are normal from my place and thus okay. 

Now that I know ping times are okay in safe mode, how do I hunt down, what might be the issue with my MBA in normal mode? Any clear procedure you advise?
This issue affected several people after upgrading to Mountain Lion. For many, reducing their MTU size solved the issue:


Open System Preferences.
Select Network.
Select your connection and choose Advanced...
Select Hardware.
Change Configuration to Manually
Reduce the MTU size to 1300. Most people had good experiences with this value.
Observe how ping behaves over time. You can further reduce the MTU size in steps of 4.


However, there seems to be another issue: Proxies. The solution suggested here is:


Open System Preferences.
Select Network.
Select your connection and choose Advanced...
Select Proxies.
Turn off Auto Discovery Proxies.
Apply the settings.


But this should be fixed with an upgrade to OS X 10.8.1 (not sure if an upgrade to Mountain Lion directly brings you to the latest upgrade, or to 10.8.0).

Actually, I would first try the upgrade to 10.8.1. If this does not work, try the proxy solution. If this does not work, try the MTU size reduction.