Use this instead:
$('#save').click(function () {
$('#mytable').find('input[type="checkbox"]:checked') //...
});
Let me explain you what the selector does:
input[type="checkbox"] means that this will match each <input /> with type attribute type equals to checkbox
After that: :checked will match all checked checkboxes.
You can loop over these checkboxes with:
$('#save').click(function () {
$('#mytable').find('input[type="checkbox"]:checked').each(function () {
//this is the current checkbox
});
});
Here is demo in JSFiddle.
And here is a demo which solves exactly your problem http://jsfiddle.net/DuE8K/1/.
$('#save').click(function () {
$('#mytable').find('tr').each(function () {
var row = $(this);
if (row.find('input[type="checkbox"]').is(':checked') &&
row.find('textarea').val().length <= 0) {
alert('You must fill the text area!');
}
});
});