The tiny lines are a screen redraw error. Illustrator artwork is (usually) vector and therefore resolution independent but in order to display vector graphics on your screen it must be interpreted to fit into a pixel grid. Sometimes at certain magnifications the math gets a little wonky and those lines appear along vector edges but they are not a part of the file they won print and if you zoom in or out from the magnification where youre seeing them they should disappear. Nothing to worry about.