Can rice eaten on the second day be dangerous?

Assuming that you mean it was left out (refrigerated it's clearly fine. Rice keeps for a week), it is probably fine. Unless it's really warm and damp in the room, you probably will not see any mold on it in a single day. Keep in mind that if it was boiled and then left alone, it is virtually sterile so it'd easily last a day. If it was touched with utensils/food, just check for anything growing. If not, nothing serious enough to be truly harmful will be there.