Well, it's clearly not a number since it has dashes in it. The error message and the two comments tell you that it is a factor but the commentators are apparently waiting and letting the message sink in. Dirk is suggesting that you do this:
EPL2011_12$Date2 <- as.Date( as.character(EPL2011_12$Date), "%d-%m-%y")
After that you can do this:
EPL2011_12FirstHalf <- subset(EPL2011_12, Date2 > as.Date("2012-01-13") )
R date functions assume the format is either "YYYY-MM-DD" or "YYYY/MM/DD". You do need to compare like classes: date to date, or character to character. And if you were comparing character-to-character, then it's only going to be successful if the dates are in the YYYYMMDD format (with identical delimiters if any delimiters are used).
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