I'm pretty sure I found the issue already.
Flarum still has some bugs regarding relative path linking, meaning that mentions for instance will not append the /forum/ to the links. This is reported already on Github, can't find the ticket right now though.
Google actually does index the forum properly, however due to these wrong links with mentions, answers etc. it also causes lots of 404 to be thrown.
This issue will hopefully be fixed with beta5.