There are no double vertex and I have no clue how to fix that...
- First problem
The order of the modifiers is important.
In your example, the quarter is first smoothed by the Subsurf, then duplicated by the Mirror.
If you put the mirror first (with the arrows right to his name), the quarter will be duplicated, then the whole table will be smoothed.
- Second problem
You have an edge inside the model, it connects the vertex at the center of the hole, with a vertex above (the center of the table, i think). Removing it should fix the hole.