Here’s a screenshot from my achievements inbox:
The rep gain on the Meta question has the
” rendered correctly, but I see plain HTML entities on the badge notification.
I found a couple of similar questions about rendering in badges being different to rep changes, but I couldn’t find one that specifically mentioned special characters.
I can see the problem in Safari 8.0 (10600.1.25) and Chrome 38.0.2125.101, both on OS X 10.10 (14A388a), but the quotes are displayed correctly in the latest public version of the iOS app.