Error in link URL can result in 404 web page not found and this is not good for both website visitors and search engines, visitors will have an impression that your website is not properly maintain and drop confident of the information given in the web page, search engines feel the same and may lower the quality score of those web pages with broken links.
Visitors and search engines activities on your website are all log in your website traffic log file, any web hosting provider will have options to either download the raw log and parse with the web stats analyzer of your choice, or use the web stats program provided for the hosting account, both are ok so long you can check the website traffic information.
You should practice checking web stats periodically and look into the search engine crawling stats to ensure there is no broken links found in your website. There are lots of tools out there that can also help you check links within your website, a widely used tool for link checking is Xenu link checker, run a scan with this tool periodically can help you find broken links in your website quickly.
A good website will always be clean from any broken links.
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