Believe it or not, half of web traffic is from bots. Below are some actions you can take to manage 404s.
Monitor and redirect 404 errors to the appropriate place
The best thing to do is to make sure you are monitoring what is going on, so you can create redirects as needed. The redirection plugin will both monitor the most frequented 404 URLs, and allow you to create redirects for them.
Reduce random 404s by rate limiting malicious bots
Wordfence has a feature that allows you to rate limit anyone who visits too many 404 pages in a minute. In addition as you research and take proper security measures on your site, there will be less malicous bots adding 404 errors you don’t care about.
You might be getting all of those 404 errors from bots. The best way of dealing with 404 errors is to install the Redirection plugin and let it track the most common 404 errors, so you can redirect users to the appropriate place. Some 404 errors will be from bots trying to hack you, you can ignore these. The ones that matter are the ones that are being triggered by humans and search engine crawlers.
Crawl the site for broken URLs
Use a link checker such as http://wummel.github.io/linkchecker/ to crawl the site for broken URLs.
Get 404 alerts from Google
This is actually possible. When you connect your site up with Google Search Console, Google will warn you if they might remove a page from it’s system because it turned into a 404. You can then redirect the pages to the appropriate place, so you don’t lose any SEO juice from that page. Note: Google no longer reports all of the broken links it finds, just the 404 errors that threaten a page’s removal from Google’s index.
Changing the look of 404 pages
This is unfortunately controlled by you WordPress theme. You’ll need to check your theme options, but most themes don’t give you that much control over the 404 page. If you really wanted to, there are plugins that allow you to change the 404 page, but be careful about installing too many plugins and slowing down your website.