So I have this fairly simple ring object, and it's not nearly smooth enough for what I need to use it for. However, when I subdivide it it creates these two strange gaps on the side/inside of the object. Does anybody know why this is? How can I fix or avoid this?
You have a couple of coincident, but un-welded vertices there.. maybe not caught by a Mirror 'Merge' setting? Use M Merge in one way or another to glue them together.
By the way, topology like this will yield smoother curvature under subdivision, and be easier to work with...
(This one's just a latitude face-ring nicked from a UV sphere, extruded and bevelled)