Adam, it sounds to me like your pile is pretty well done. Remember that it is normal to screen compost for use in potting, which should tell you that even "finished" compost is still going to have some bits and pieces.
Now, if by recognizable you mean that a carrot slice is still identifiable and that lettuce leaf just looks wilted - well, no, that would not be finished
But some sticks, a few leaves that still look like leaves, that can be expected in a finished pile.