Checking the Platform Update Version from the client is easy:
Click the questionmark icon in the top right corner and select "About" to see the version info.
But what to do if the client is not available (for example because a build is failing)?
In earlier versions it was possible to just check the file version of CIL compiled DLLs (AX 2012) or even AOS files (before AX 2012).
I found a way to check the Platform Update Version in Dynamics 365 FSCM:
Navigate to this file:
K:\AosService\WebRoot\AxHost.exe (drive letter
K for cloud hosted environments,
C for locally hosted ones), right click it, select the tab
Details and check the property
If that file does not exist for whatever reason,
AosService\WebRoot\bin\Batch.exe can also be checked.