I read through the achievements bugs thread but didn't see anything on this particular issue. I'm not really sure if this achievement is a bit messed up (most "feed your pet this kind of item" requires you to feed them ALL of that kind, not just one) or if it just isn't showing that I have the achievement:
http://www.majhost.com/gallery/BlueLeafeon/Temp/untitled.jpg
It seems to be working as it should. These new achievements are still of the feel your pet of ALL of the items variety. The description does say "Feed one of your pets all of the following pies", rather than "Feed your pets one of of the following pies".
you have to feed your pet all off the items on the list to get the achievement :) So it seems to be working ok, as long as you haven't actually fed those items to your pet!
it is showing your progress. You fed that one item and you still need to feed all the others shown. So it is working as it should.

Then why does it have a 0/1 there? That seems a bit goofy to me.
that part tracks the achievement itself. So it's 0/1 achievement. When you get the achievement, it will say 1/1. It's like when there are tiers, it will say 0/5, 0/10, 0/25, etc. and as you complete the achievement, the tiers fill in. Make sense? :D