What is the little, grey, rectangular stone with a sheen in my "Latest Reputation Received" window? Is it negative rep? 'Cause the comment with it is pretty positive.

It was likely given by a new member with no rep power, thus the neutral grey.

Mike

If it was negative rep you would have noticed your rep lowered, not a fun thing when it happens to you.

I too have experienced the little grey icon.

Like MiketehFox said, it's somebody who has no rep power yet, trying to give you positive rep. Since they have no rep power you experience no rep change at all and just get a little grey icon and a nice comment to read.