Use the built in "Inspect Element" in Chrome or other browser.
Move to "Console" tab and it will spit out every error.
Now, if you're talking about optimizing, you can use the "Network" tab and look at large files, bottlenecks etc.
And then there's the "Lighthouse" tab which will show you how things render in Google's eyes. This is a clean insight to speed, SEO scores etc.
In many ways, it's better than using some of the websites like pingdom, gtmetrix, etc as you're getting RAW data from YOUR location. Using a website, you're relying on their location and sometimes faster network speeds as they are making datacenter to datacenter calls.
however seositecheckup will only let you run some free checks and then ask for money, you can run one of a check and download its pdf report and start fixing the errors from there, at least this is where I started.
Google Search Console is my go to, but I have never used anything else. This is the first time I have heard of GTmetrix and I will be giving it a try right now. Thank you!
Some potential free website error checker tools include Google Search Console, which identifies crawl errors and site issues, Screaming Frog (limited free version) for comprehensive error detection, and W3C Markup Validator for HTML validation.