Here's the updated code that checks the checkbox, but why when I click on the J5 cell does it do the following:

1st click - selects cell J5
2nd click - starts edit on J5
3rd click - exits edit on J5 but also checks the checkbox in the NextRound column because it receives a click event behind the scenes

Why does the first cell of the row receive a click event when leaving another cell?

cellClick: function (evt, ui) {                        
if (ui.colKey === 'NextRound') {                            
var myCell = grid.igGridSelection('getCellValue', ui.rowIndex, 'NextRound');                            
var dataview = grid.data('igGrid').dataSource.dataView();                            
var myVal = dataview[ui.rowIndex]["NextRound"];                           
grid.igGridSelection('selectCell', ui.rowIndex, ui.colIndex);                            
grid.igGridUpdating('startEdit', ui.rowIndex, ui.colIndex);
grid.igGridUpdating("setCellValue", ui.rowIndex, 'NextRound', !(myVal));
dataview[ui.rowIndex]["NextRound"] = !(myVal);                        
}

Much appreciated. Using your code still allowed the user to accidentally check the checkbox by clicking another cell 3 times though (even slowly - 1= select, 2=edit, 3=exit edit but check checkboxes)  I was able to get around both issues by dropping the cellClick event and switching to using the cellSelectionChanged event off the Selection behavior. 

{ name: "Selection",
                            mode: "cell",
                            multipleSelection: false,
                            activation: true,
                            cellSelectionChanged: function (evt, ui) {
                                var actualRowIdx = ui.cell.row[0].sectionRowIndex; // rowIndex is not zero based, but other methods are and expect a zero-based index (Infragistics says to use undocumented ui.cell.row[0].sectionRowIndex)                                    
                                if (ui.cell.columnKey === 'NextRound') {
                                    var myCell = grid.igGridSelection('getCellValue', actualRowIdx, 'NextRound');
                                    var dataview = grid.data('igGrid').dataSource.dataView();
                                    var myVal = dataview[actualRowIdx]["NextRound"];

                                    grid.igGridSelection('selectCell', actualRowIdx, ui.cell.index );
                                    grid.igGridUpdating('startEdit', actualRowIdx, ui.cell.index );

                                    grid.igGridUpdating("setCellValue",actualRowIdx, 'NextRound', !(myVal));
                                    dataview[actualRowIdx]["NextRound"] = !(myVal);
                                }
                                else{
                                    grid.igGridSelection('selectCell', actualRowIdx, ui.cell.index );
                                    grid.igGridUpdating('startEdit', actualRowIdx, ui.cell.index );
                                }

                        }
                        }

The only problem now is that clicking on a checkbox cell a second time seems to enter edit mode and results in a blank field (looks like a text box but doesn't accept text) which sticks around until another checkbox is put into the same state or the page is refreshed.  Any thoughts on that one? 

Thanks for the link to hilite.me it's pretty awesome and made the above code look so much better in this forum - and copying it isn't a big deal, I was already having to copy to notepad, then copy from there and paste into the forum and redo all the lines to get around the double-spaced line breaks which are the default.

Here is the configuration of the Selection feature that I can recommend:

{
    name: "Selection",
    mode: "cell",
    multipleSelection: false,
    activation: true,
    cellSelectionChanged: function (evt, ui) {
            var actualRowIdx = ui.cell.rowIndex;
            //if (ui.cell.columnKey === 'NextRound') {
            //debugger;
            if (ui.cell.index == 0) {
                //var myCell = $('#grid1').igGridSelection('getCellValue', actualRowIdx, 'NextRound'); // As I mentioned earlier in the forum thread, igGridSelection does not have a getCellValue API method.
                var myCell = $('#grid1').igGrid('getCellValue', actualRowIdx, 'NextRound');
                var dataview = $('#grid1').data('igGrid').dataSource.dataView();
                var myVal = dataview[actualRowIdx]["NextRound"];

                $('#grid1').igGridSelection('selectCell', actualRowIdx, ui.cell.index );
                $('#grid1').igGridUpdating('startEdit', actualRowIdx, ui.cell.index );

                $('#grid1').igGridUpdating("setCellValue",actualRowIdx, 'NextRound', !(myVal));
                dataview[actualRowIdx]["NextRound"] = !(myVal);
            }
            else{
                $('#grid1').igGridSelection('selectCell', actualRowIdx, ui.cell.index );
                $('#grid1').igGridUpdating('startEdit', actualRowIdx, ui.cell.index );
            }

    }
} 
and here's for the Updating feature - I've just set a handler for the editCellStarting event so that I can cancel it if we're on the NextRound column: [code]
{
    name: 'Updating',
    editMode: 'cell', 
    enableAddRow: false,
    enableDeleteRow: false,
    editCellStarting: function(evt, ui)
    {
        if(ui.columnKey == "NextRound")
            return false;
        
        return true;
    }
}