Checking On page errors "manually" is the best method. But to save your time, there are several tools that can be used such as:

validator w3
brokenlinkchecker
deadlinechecker
404checker

I'm also needing the same help. I'm so glad that I saw this thread.

Thank you so much for your suggestion, Sir.

I'm also new to SEO that's why I'm not very familiar with some helpful tools. I still have a lot to learn.

Fortunately for me because I find this information is confirmed

I think the most of the people using Google web master tool to check them on page error.

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To test the fault of the page, you should consider it by hand is better! Then you can have more experience! Apply for next time!
But I believe 404checker, it's a very good tool for you there!
Good luck!

SEO ON Page checker tools are:

• Google Webmaster Tools
• Screaming Frog SEO Spider
• Broken Link Checker
• Dead Line Checker

I often use following tools to check my website onpage performance varvy.com, Iwebchek, W3c validator, Google page speed insight

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Google Analytics for website traffic pattern
Google Webmaster for website health
Google Keyword planner, Trends, ubber suggest for keywords research
Alexa Rank also suugest you about website traffic
small seo tools to check PA and DA of website
Buzz Sumo to generate content ideas
Hootsuite for managing multiple social media accounts on single platform
Copyscape to check duplicate content
seomastering to check trust rank of website
multipagerank to check page rank of website
Used webconfs to analyze keywords density

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You can optimize your website on WooRank, Broken link checker and Website Crawler tool. These tools are good for checking site's on page error.