When inspecting my clanmates on the Companion App everything is working fine, except for one of them, on which I can't see any of his characters. Already tried re-inviting him and didn't work. Any thoughts?
You will not be able to inspect people's characters from their Bungie.net profile if they have chosen to not show their linked accounts on their public profile'.
You can ask that person to go to 'Profile->Settings->Linked Accounts' and check 'Display on public profile', or you can search for their gamertag (if you know it) and view them directly.