For one of my sites Google webmaster is showing duplicate meta description and title for couple of pages. Can we just ignore that or change them?
It seems your pages and posts are using the same Meta Description and Titles.For each page and post,you change the Title Tag and Description.
if there short texts in tags it's very difficult make it unique, and also don't think it's so important many sites have same problem and get huge G traffic. And sure, if there small count of pages in your website - make them unique, wouldn't be worse
You can ignore them, but better solve the problem and don't risk some pages being dropped from their index. Make sure you only allow indexation/accessing of each page via a single URL only. If you're dealing with some sort of a CMS like WP, try taking advantage of the canonical tag in your themes header or using an seo plugin that will take care of this. Sometimes, this could happen with paginated results in your listings, you don't need more than one page for your category, as long as you're submitting a sitemap or have a link to every item in your category somewhere in your site.
Currently Im having good keyword serp for those pages so now if i make a unique title and descriptions for those pages will my keywords serp drop?
You'd better have UNIQUE title and description for EVERY page of your website... Yes, this is boring, but would be really successful, because it helps EVERY page of your website rank higher in Google, not just the homepage!!!
50/50 but now - while update is still going i think 90% for drop. in updates time don't forget the rule: work - don't touch
You have to do some practice on your titles & Description which are giving same meaning but try to maintain unique titles & descriptions it will help you for better rankings...