сделать step локальней
$(document).ready(function () {
var image1 = new Image();
image1.src = "img/1.png";
var image2=new Image();
image2.src = "img/2.png";
var image3=new Image();
image3.src = "img/3.png";
$("#tap").click(function () {
setInterval(slideit, 20);
});
function slideit() {
var step =1
if (step<3){
document.images.slide.src = eval("image" + step + ".src");
step++ }
}
});