I had a user bring up the fact that google was indexing www.domain1.com/shorturl1 correctly, but also www.domain2.com/shorturl1 (which points to the exact same content from the correct URL). After testing, it appears I can duplicate this problem across nearly every domain that we host.
Has anyone run across an issue like this before? Appreciate any insight
This could be due to numerous reasons, although ultimately it means that you have a page that is accessible via multiple domains and that a canonical URL has not been specified. Typically speaking, if the content and host is the exact same for a given page and the only difference is the URL, search engines will eventually pick a canonical URL for you so that you can't game the system by having multiple results in the SERPs for the same page.
Due to how configurable and flexible Sitecore is in terms of sites / domains / languages / etc, one must always be mindful of all of the different ways a page might be accessed. Many different layers of the stack can affect this. DNS, WAF, load balancers, web configs, robots.txt, noindex meta, custom redirect functionality, specific site configs, custom code pipelines, different environments with different domains, etc.
In general, try to ensure that a specific page can only be accessed via one canonical URL. This is often done with redirects, or by specifying the canonical URL in a meta tag.
Without more information it's difficult to tell what the best fix may be in your case, but you can read these posts to get a better sense of canonical URLs and Sitecore.
https://www.getfishtank.com/blog/why-your-sitecore-site-needs-canonical-tags
https://www.getfishtank.com/blog/using-iis-rewrite-module-to-force-redirect-to-a-secure-canonical
