ETA, I have no idea why it’s so small, but you can see the icons there between the reply box and the buttons.
ETA, just for kicks, try going back to that page (where you would be replying (Go Advanced)) and hit Control-F5. It’s a long shot, but refreshing the page might be all you need.
It appears that the Straight Dope Chicago forum has post icons turned on (none of the other forums do) – there’s a toggle in the forum permissions that probably got left on (the default) when they created the forum.
As for why some people can see it/set it when posting and some can’t, post icon permissions can be set per usergroup, so mnemosyne’s hypothesis is likely correct: it’s on for Charter Members, off for regular members and guests.