BTW, I also tried changing the Theme from WooThemes' Athena to the "Twenty Twelve" theme with no effect. The placeholder text for "Event Date" still says "Month/Day/Year" and when I edit an existing date it does not display the century.
I even went so far as installing a fresh copy of WordPress 3.5.0 on a domain I was not using. It still looks the same.
I tried in a few different browsers and believe I've discovered the issue is in the way Google Chrome handles INPUT field with a type of "date." Chrome appears to be one of the few browsers that has support for generating a date picker automatically for INPUT fields of type date. However, it uses a placeholder based on the localization settings set when you select your language.
Browser support for the INPUT type of date, which was introduced with HTML5, is still limited based on what I've found (Chrome, Safari, Opera): http://www.w3schools.com/html/html5_form_input_types.asp
Also worth noting is that the "placeholder" attribute you are using in the INPUT form field is not supported for the "date" type as best I can tell: http://www.w3schools.com/html5/att_input_placeholder.asp
From that page "Note: The placeholder attribute works with the following input types: text, search, url, tel, email, and password."