As it is not easy to find each and every broken link on your blog, so you can rather use this simple tool which can easily scan your blog for broken links:
After checking your blog for the invalid links, simply either edit or remove them.
Other than this tool, there is an other way too. You can sign up at Google Webmaster tools, where you have to submit your blog’s sitemap. Then with frequent updates and reports from Google, you will be shown a list of links on your blog, which no more exists. But these are ONLY those links which are on your own domain. So it is better to use both of the explained methods.