Is it possible to update multiple Nintex for Office 365 apps in one operation somehow or do we have to visit every single site where the app is installed and do it there?
We are using both the Forms and the workflow app on many sites and it is a potential nightmare to have to do the app update on every single site.
Unfortunately there is no way to update all of the sites all at once.
Updates are only required when the app requires new permissions than it previously had due to adding new functionality. This is why when you select "update" and click "Get it" SharePoint will ask you to "trust it" when getting the new update.
With that being said this "update" process will not need to be done every time we release an update to our office 365 products, just when our products require additional permissions. Until the product gets updated these new permissions only the new functionality will not be available however the existing product will remain functional.