Question

If I type

DateString[{2011, 2, 29, 0, 0, 0}, {"DayName"}]

It gives "Tuesday".

And also,

DateString[{2011, 2, 29, 0, 0, 0}, {"DayName"}]

DateString[{2011, 3, 1, 0, 0, 0}, {"DayName"}]

Answer 1

Needs["Calendar`"];
myDay[x_List] := DateString[x, {"DayName"}] /; DateQ[x]  

myDay[{2000, 1, 1}]
->"Saturday"

myDay[{2000, 13, 13}]
->myDay[{2000, 13, 13}]  

Of course you may throw a message (or Abort[], or whatever) if you want to :

Needs["Calendar`"];
Clear@myDay;
myDay[x_] /; If[DateQ[x], True, Message[myDay::nodate, x]; False] := 
                                                       DateString[x, {"DayName"}]
myDay::nodate = "The argument `1` is not a valid date.";