Writing this for myself. I've worked with a stack of clients recently whose XML sitemaps are broken, very, very broken. There's so many different things that could go wrong so I'm writing them down so I can work through them in future...
XML SITEMAP BASICS
Does the client know what an XML sitemap is?
What's the URL of the XML sitemap?
Are you sure the client is not confusing it with a HTML sitemap?
Is the XML sitemap manually or dynamically generated?
Is the output of the XML sitemap regular code, or displayed via a plugin?
Is it one XML sitemap or are there multiple sitemaps? (e.g image sitemaps)
If multiple sitemaps are used, is there a sitemap index, or are the sitemaps completely separate?
AWAY FROM THE SITEMAP
Are the XML sitemaps submitted to Google Search Console?
If yes, is Google Search Console able to read the XML sitemap?
Does the number of URLs displayed in Google Search Console correspond with the number of URLs you would expect to see on the site?
Is the XML sitemap referenced in the robots.txt file?
THE CODE OF THE XML SITEMAP
Does the sitemap actually have URLs listed in it? i.e check it's not empty
Are there more than 50,000 URLs in a single XML sitemap? (If so, split it up)
Is the XML sitemap more than 50mb in size? (if so, sort it out)
Does the XML sitemap consistently load (and not throw any random 410 errors)?
When was the XML sitemap last updated? Do the dates show it is dynamically updating?
Is there a <lastmod> tag?
Is the <lastmod> date configured correctly?
Is there a <changefreq> tag?
Do the change frequency settings look correct given what you know about the website?
Is there a <priority> tag?
Do the priority settings look correct given what you know about the website?
Are the URLs submitted all absolute urls? (this is what is needed) (https://www.danieljameswhite.co.uk/about)?
Are any URLs submitted relative urls? (this is what is not needed) (/about)?
Are the URLs showing the correct site protocols? (ie www. and https)
Is the same URL showing up more than once in the sitemap?
Are there any sitemaps holding URLs for parts of the website we don't want included (blog tags etc)
Is there any other random code/schema included which shouldn't be there?
THE URLS IN THE XML SITEMAP
Are there any URLs included which return a noindex tag?
(If so, adjust, depending on desired outcome)
Are there any redirected URLs included in the sitemap? (If so, remove them)
Are there any non-canonical URLs included in the sitemap? (If so, remove them)
Are there any URLs with parameters included in the sitemap?
(Adjust or keep, depending on desired outcome)
Are any Orphan URLs being included in the sitemap?
(If so, keep them. Try to link to from main website)
Does the XML sitemap show any image URLs associated with each page?
Are the image URLs correctly configured? (No parameters, duplication etc.)
For international sites: Are all local variations of pages included in respective sitemaps?