[SalesForce] Dataloader error : Error converting value to correct data type: Failed to parse date: Yes

It looks like the CSV file has the dates in mm/dd/yyyy format rather than dd/mm/yyyy. Hence the invalid date exception with the 31st month.

This will work:

date parsedDate = date.parse('31/5/2013');

This will fail with "System.TypeException: Invalid date: 5/31/2013"

date parsedDate = date.parse('5/31/2013');

From the Date.parse methods docs:

Constructs a Date from a String. The format of the String depends on the local date format. The following example works in some locales:
date mydate = date.parse('12/27/2009');

You can find the locale Date format information in the Supported Locales docs.

Another option would be to use the date format YYYY-mm-dd and date.valueOf().

Can you try this? Copy and paste the whole list of account names in Editplus, open a fresh excel sheet, copy back the list from editplus and paste it in the excel sheet. Then save the sheet as CSV.