The one major issues I have seen for some users is those who have a lot of old software, including some printer and other peripheral drivers, that is still 32 bit. See:
32-bit app compatibility with macOS High Sierra 10.13.4 and later - Fairly complete FAQ - https://support.apple.com/HT208436
Catalina did away with 32 bit support so people who have software such as Microsoft Office 2011 are finding they now have to subscribe to Office 365 or find alternative Office package. Apple has its own free Pages, etc., and there's free LibreOffice and OpenOffice.
The other thing I have seen are reports from people who have older printers or projectors. Some companies have simply ignored long-time advance notice this has been coming and those users are left with devices that are not seeing updated drivers.
Then there's other legacy software such as something highly specialized where the developer simply stopped upgrading or is maybe no longer alive. The only thing to do there is to either not upgrade at all (but eventually you will have to since new Macs will require Catalina or newer), or to have a separate boot system for running those. Or maybe a variant on that and run an older operating sytem version in a virtual environment using something like Parallels.
You should review your position. Maybe you don't need Catalina yet. I never see any harm in letting the early adapters rush in and do the bug testing, then wait a month or two and then install something. ;-)