If you like doing things in Google Analytics, there’s a quick exercise you can undertake with that can reveal possible broken links and information about them. It requires that your site has a proper error (‘404’) page, and takes advantage of the fact that this page has a title.
What you do is to find out the title of your error page, by taking a look at the page itself. Then search for that title in the ‘Page Title’ report under Behaviour > Site Content using its title. The search filter box makes that easier. Next, click on the title in the list, and you’ll get a ‘page’ (i.e. URL) report for pages with that title (the error page). These are the URLs that people were using that caused the error page to show.
Many will be one-offs, probably mis-types, and may not be worth worrying about. However, if one or more has been hit several times, that suggests a broken link either on your own site (fixable!) or on another site. Either way, I’d set up a 301 redirect to prevent any future issues.
As I mentioned, this only works if you have a proper error (‘404’) page. You should have one: something that matches the style of your site, with a helpful message, like this. If you’re not sure, try typing in a non-existent URL on your domain ([your-domain.com]/dfkhgdsfhgdhsfg) and seeing if a nicely-formatted page comes up or an unhelpful 404 error message.