I have the objective to raise any special stat of any 14 dwellers. I found that not all have been ticking the counter for that objective. Most recent that I noticed not counting a tick was from the Weight Room, and Fitness Studio. Noticed too that those dwellers have a maxed charisma skill, may be related but shouldn't make a difference.

probably because you already leveled them up for that same achievment

Yep, you must level up 14 different dwellers a single special point, not a single dweller 14 times.

Same as "Gear up X dwellers". You may use the same piece of clothing (equip, then unequip), you just have to do it on X different dwellers.

Easiest way? Train dwellers with 1-2 in any stat. Takes the least amount of time.

The objectives are probably the most annoying part of the game, though the most look forwarded to. I honestly love doing them but they have some, like this, that I'd considered to be bugged. Why does it matter that I raise the SPECIAL of one dweller 14 times or 14 dwellers one time? And why does it have to be new dwellers? I mean seriously if I'm using old dwellers that have done it before, the logic would be it would take longer to do the objective thus I'd want to use newer dwellers where I can but the game shouldn't hold it against me for using older dwellers.

Same goes with the gearing up objectives and the assign x dwellers to the correct room objectives.

Bottom line, they need more varied objectives and to fix these 'bugs'.

I found that in the objective if there is written Dweller (with a capital D) then it's usually any at all... when it's written as dweller (small d) then unique persons.

I used new dwellers, upon starting game up the next day no credit toward quest, this has happened more than once.