It's also happening on mobile browsers. I use Chrome on my phone and it changes out the apostrophes.
Without knowing anything about how this site works, I imagine it stores posts into a SQL database of some sort and there is some code in the receiving of data to combat SQL injection that is changing the apostrophes into question marks.
When your tech has time to look at it, he might check around there.
Of course if your code is super complicated finding the exact spot could be a nightmare.
As it is, it's something I can work around.