DateFormat.parse(String, ParsePosition) returns null when the string is invalid. That can be used:
Not only does this code not throw an exception, it also doesn't create an unnecessary Calendar (and Date from getTime()) object. You can improve this code slightly by checking if the entire String is used in parsing:
If the parse position's index is not directly at the end of the String there is something else in the String as well. This will occur if the passed String is something like "20/05/2010abc". The added check will make the method return false if that's the case.