Hello darshanaasodekar, and welcome to the forums.

There's nothing you can do about this - Google sometimes does revert to earlier data. You know they've got a newer cache for your pages, so you can relax about it. If you don't already have a Webmaster Tools account, I'd suggest you open one. That data can be quite helpful and often gives you information you can act on.

What I am seeing is even weirder. Google is probably showing years old cache. I had suggested G to not show the DMOZ description but suddenly it has started to show it this weekend.

Thank you so much for the details! I'll surely look into getting a webmaster tools account.

Is there any different way to get Google to update their old cache, so that new pages are indexed?

The cache and the indexed content do not always line up with each other - I have seen them come from different versions of a url. But in either case, I do not know of any way to force an update to either the cached page or the indexed content.