Simply remove the colon ":" from the definition of g. With the colon, you will call the gradient when the variables w0, w1 are numerical, instead of symbolic, whence the errors. Here is the code with a couple of minor simplifications:

RSS[x_List, y_List, w0_, w1_] /; 
  Length[x] == Length[y] := (y - (w0 + w1 x)).(y - (w0 + w1 x)), 
GradientDescend[X_List, Y_List, initialIntercept_: 0, initialSlop_: 0,
     u_: 0.05, tolerance_: 0.01] /; Length[X] == Length[Y] :=

  Module[{wList = {}, w0, w1, gr, k = 1},
   gr = Simplify /@ Grad[RSS[X, Y, w0, w1], {w0, w1}];
   w0 = initialIntercept;
   w1 = initialSlop;
   While[Norm[gr] > tolerance,
    {w0, w1} = {w0, w1} - u gr;
    Print["Iteration ", k, "======>", {w0, w1}];
    wList = Append[wList, {w0, w1}];
    k++;];
   wList];