We get the NullPointerException 'MetadataAssetApplication.java:73' when trying to check out an asset. But it is still possible to use the function "edit metadata in same version...".

We know that error when the value for "application" is missing in the meta data. You can check it when you have a look into the asset xml.
As a workaround, use "edit metadata in same version..." and set a value for the application. To find the root cause, check how that asset was created. Mostly it happens when the asset was created by an interface. Check and correct the interface.