Ken, i did something similar to an Ikea dining table about 3 years ago, except without the big booboo. The table came out quite nicely for one of my first major wood finishing projects.
You may hate my answer...but...here's my amateur recommendation: You really should sand down the entire face area that contains the little mistake, restain then re-poly.
If you try to restain just the spot, you might be able to make this patch work but i'm guessing it may come out rather visibly different than the rest of the side.
Note to self for future: i hand sanded the poly between coats LIGHTLY just to remove surface bubbles (micro bubbles at that) just as Bigwill suggests. Think of it like a car polish at this stage. The hand sanding takes longer, but you lessen the chance you will go through the poly coat.
After the first sanding and cleaning, the 2nd poly coat should feel alot more solid and thick. By the third coat, it should be as smooth as Peter's baby's bottom.
