It may mean "side" in modern Israeli Hebrew, but in ancient Hebrew, "pani" means "face" or "surface." For example, in Gen 1:2b it says "...v'Ruach Elohim m'rachepheth al pinay tehom" or "and the Spirit of God hovered above the SURFACE or FACE of the deep." It does not say the Spirit of God hovered over the SIDE of the deep. That would not make any sense at all.
It is true that Hebrew does not speak of a personal "face" in the singular form. It is always "paniym," or "faces." However, since G-d is the same yesterday, today and forever, He does not have many faces like humans have. Therefore, it is fully appropriate to speak of God's face as singular.