I am formatting a date in the following way:
date = new Date(\"2013-05-12 20:00:00\");
formattedDate = new Date(date.getFullYear(),date.getMonth(),date.getDate()
I think you need a 'T' between the date and the time to get it working fully.
date = new Date("2013-05-12T20:00:00");
There are quite a few possible datetime formats allowed in the spec and I don't think all browsers offer all possibilities. For Firefox see https://developer.mozilla.org/en-US/docs/JavaScript/Reference/Global_Objects/Date/parse
To be really safe cross-browser you might want to try the RFC2822 / IETF date syntax (basically the same as Chrome spat back out at you)