"Join Button" Missing on Skype for Business Mobile App and on Outlook for random users

That's a tough one to diagnosis.  In the past, this usually means that the Skype metadata that is being added to the meeting invite via the Outlook plugin is being stripped or missing.  Without this metadata the Skype Join Button does not appear.  Typical reasons for this range from when the organizer copy and pastes meeting information from invite to invite (most common) or (less common) where a 3rd party add-on service is stripping it out.

1. My first approach would be to validate that the UC metadata is actually in the affected meeting invite using a tool like http://mfcmapi.codeplex.com/releases/view/629707.  If it's missing you'll need to investigate the why.  If you are using Exchange Server ensure that the service is allowing trusted https://blogs.technet.microsoft.com/jenstr/2013/04/08/join-button-missing-on-lync-meetings-from-federated-partners/to be received/delivered with federated partner organizations like Microsoft.
2. If you see the UC and Online Meeting metadata in the "affected" meeting but are still not seeing the meeting join button I would then verify you are on the latest version of the SFB iOS mobile client (6.10) and the SFB PC client (Nov 2016). 
3. If the problem still exists and 1 and 2 are true then I would open a case with support to get some help.

Take note of any common similarities between the meetings with the missing Join button.  Ask questions like who sent the meeting invite, what version of Office is the organizer using, is the organizer internal or external, etc...?  Keep track of this data and you might find that there is a common thread among the meetings.

"Trust but verify" is my philosophy.  Just because the user "says" they are not copy/pasting the meeting information doesn't mean they are following the correct procedure to create the meeting.

Good luck.