rp_ge[$(this)[0].p.id] = p;

It appears that neither IE7 or IE8 knows what "this" is in the context.

I'm not good enough with javascript to fix this. 

First, I use a custom formatter to add a "edit" icon to the grid:

formatter: function (cellvalue, options, rowObject) {
					return editButton(rowObject.Id);

function editButton(id, grid) {
	return "<input type='button' value='&nbsp;' title='Edit row' class='grid-button grid-edit-button' onclick="editGridRow(event,'" + id + "');" />";
}

Then I call the editGridRow function like this:

function editGridRow(event, id) {
    var button = $(event.target);
    var grid = button.closest('table');
    grid.jqGrid('editGridRow', id, editGridRowOptions);
}