My inventory doesn't show all of my items, including trophies, rarites, and other uber stuff. It also sometimes multiplies the items, like it said I have 8 First Place Trophies at one point, while I only have 1.

Are you using any plugins?

Yes.

Try uninstalling all plug-ins and see if the problem still persists.

Also, does it happen while looking at the inventory tab of the PDA (sorted by location or by type?), the Load/Unload tab, the commodity sell tab, or a plug-in like StationFind? (A screenshot might help in this regard)