Start by setting the other specify to not require a response in the list settings. Then set the custom JavaScript verification (found by clicking the "Advanced..." button in the grid question settings) to this:
if (SSI_GetValue('GridQ_r10') == 1 && SSI_GetValue('GridQ_r10_other') == '') {
strErrorMessage = 'Error message here.';
}
"GridQ" should be replaced with the name of the grid question. "r10" should be updated with the row number that has the other specify.