[Deff]

var employees = {
"Вася":["30.12.2001",8],
"Петя":["11.07.2002",9],
"Коля":["06.05.2004",6]
}
function outDay(arr){
 var startDate = new Date(arr[0].split('.').reverse().toString())
 startDate.setYear(arr[1]);
 var outday = startDate.getDay();
 return outday;
}
var outArr = []
for (key in employees){
 var outDayThis = outDay(employees[key]);
 if(outDayThis==0||outDayThis==6)outArr.push(key)
}
alert('Заканчивают контракт в выходной:\n'+outArr.join('\n'))