It depends on how you want it to look afterward. If you want it to look exactly the same, (and can afford having it fixed) I'd suggest having the holes re-knit somewhere like http://www.knitalteration.com/sweater_repair.html
If you don't mind a little "flair" you can embroider a small detail over the scarf on both sides. I did this to mine and it acts as a reminder never to leave it in the garage overnight. ;)
Walker
December 2009