Those of us with these Ikea cases know that while they do keep your figures out of harms way and keep most of the dust off em they ain't exactly dust proof. To try and fill the big gaps either side of the door glass I've taken to using thin self adhesive foam weather stripping.
Take the door off and run one length on the the door jam side glass piece. Set it back about 1/4 inch from the edge of the side glass to allow the door to close and just touch the weather stripping. You just want to fill the gap not make an air tight seal.
Now do the same with the side glass on the door hinge side but set the tape back just a smidge more. The edge of the door glass has to just kiss the stripping when it swings back and forth. Test with a short strip until you get a gap you can live with and still safely open the door.
So far I've done up four of my cases and while it doesn't completely seal the case it does cut down on the dust and doesn't spoil the look of the cases. If you are careful getting the tape on straight it can look like it's meant to be there and sort of disappears from view.
Just an experiment you can try if your as crazy as me.