bind() returns type 'any' and does not type check it's arguments. e.g.

var add = function (a: number, b: number) { return a + b; };
var addString = add.bind(null, 'hello');

compiles without error and 'addString' has type any.

bind is a default way to achieve partial application so it would be great to have it typechecked properly.

Similarly for apply, the code

var listA = [1, 2, 3];
var listB = ['a', 'b', 'c'];
listA.push.apply(listA, listB);

compiles without error and listA is still incorrectly marked as type 'number[]'.

call() example:

var add5 = function (a: number) { return 5 + a; };
add5.call(null, 'a string');

Again without a compiler error.