Does your date selector automatically trigger when the user focuses on the text field? If so then, I would go with having the 'calendar' icon inside the text field as well like @ChrisF has suggested.
Some users may perceive the calendar icon to be a link to trigger the date selector, so if it is outside they have to move their mouse to click it. Unnecessary action.
So basically, if you can't have the calendar icon inside the input field because of UI limitations, then go with your option#1 and remove 'mm/dd/yyyy'
As for 'placeholder', you can refer http://www.cssnewbie.com/cross-browser-support-for-html5-placeholder-text-in-forms/ for info on browser support and work around.