Mojave introduces a new feature in its bundled tool System Information: in the Software section is a list of Legacy Software. According to Apple’s Support Note:
“If you’re using macOS Mojave, select Legacy Software in the sidebar to see all applications that have not been updated to use 64-bit processes.”
Only what you’ll see in Legacy Software is far from complete, and thoroughly misleading.

On my iMac, that is all that it lists: fourteen apps out of several hundred which are installed.

Compare that list with the details in Applications, where a great many more apps are listed with “No” to their being 64-bit. Here’s one, for example, Nisus Thesaurus, and several old apps from Nikon.

When I run my 32-bitCheck tool, free from Downloads above, it finds a total of 339 apps and components which are 32-bit only, out of 1425 discovered in my Applications folder.

Whatever Apple’s list of Legacy Software means, it doesn’t tell you which of your apps are 32-bit only and won’t be fully compatible with macOS 10.15. Neither do the alerts which Mojave displays when you open a 32-bit app for the first time, as they appear only for apps which are being put through full Gatekeeper checks because they have just been downloaded from the internet. Those 32-bit apps which you already have installed don’t get put through those checks, so never result in that warning.

I’m disappointed that Mojave doesn’t provide any better tool for identifying what needs to be replaced over the next year or so. But you should be able to rely on 32-bitCheck, at least.

(Corrected to read Legacy Software, which makes this even more disappointing, as that should include more than just applications.)