Parts storage has been a key aspect of my product development career, and has consistently frustrated me. A few reasons for my ire:

Parts cabinets are expensive. I probably spent $200 on my cabinets, which were mostly used; at my last employer, we spent over $2K on "standard duty" parts drawers, shown here, from McMaster-Carr.
Traditional parts organizers are time consuming to organize, and often aren't formatted to hold the size and quantity of parts you need to store.
Most management systems don't allow for reorganization without significant amounts of work.
Every organization & labeling system I'm aware of is disconnected from the part specs that I usually want to have on-hand when making a selection from physical inventory.
Keeping a digital catalog of parts inventory on-hand is time consuming, difficult, and totally disconnected from the location and quantity of the parts themselves.

In order for the full implications of digital product development, manufacturing and distribution to come to pass, I believe that industry will need to completely rethink how it addresses, organizes, processes and tracks parts inventory. I have a few ideas of what this will look like, but I'd like for now to focus on the requirements for such a system.

Parts should be uniquely addressable. For many of my applications, McMaster-Carr, DigiKey, Sparkfun, and Amazon product numbers would be fine. Ultimately a system like IP would probably be preferable, if only to apply uniformity and allow manufacturers and distributors of all flavors to buy into a single standard. At some point, I wonder about the possibility of addressing not only each brand/make/spec of bolt, resistor, or chip - but also addressing each physical instance of each of those categories. With the enormous addressing capacity of IPv6, this is well within the realm of possibility - we simply need to find an appropriate tracking mechanism. (Side note: IPv6 has an addressing capacity of about 3.4*10^38. In comparison, there are estimated to be on the order of 7.5*10^18 grains of sand on all the beaches in the world. That's a ratio of 4.5*10^19 : 1, in favor of IPv6 addresses.)
Physical organization shouldn't need to be hierarchical. Hierarchical systems work fine on dynamic interfaces (e.g. on the web, where they're used in conjunction with tagging and search features), but parts organization is subject to so many other forces - not the least of which is the size and quantity of a given type of item. For example: if the bolts I have on hand vary in length from 5mm to 50mm, finding a single drawer to accommodate all of them will be difficult. Much better to allow locational organization to be loose, and instead encourage browsing through a database. Put a different way: I don't see the need to institute a browsable Dewey Decimal system on my parts; I'll just search for them on my computer, and it'll tell me where I should look.
Parts on hand should be treated as a subset of parts in the world. When I'm designing a new assembly and searching for a bolt to use in it, I want to access a single interface that will allow me to search either globally (the entire catalog of uniquely addressable parts in the world), from a single manufacturer/distributor, or only from my in-stock catalog. On the other hand, when I'm physically looking at a particular item in my inventory, I should have easy access to the product specs for replacement parts and compatible mating parts.
Inventory should be tracked in real time. When I remove parts from physical inventory, my database of stocked components should be updated immediately. As sensor technology evolves, it is my hope that this will be possible with minimal user interaction (e.g. via the use of pressure, proximity, or chemical presence sensors within the parts cabinet). In the meantime, the parts cabinet itself (or at the very least a nearby iPad running dedicated software) should offer me the ability to quickly update quantity on hand.
Complete part data should be available at the part's physical location. If I'm browsing for a bolt, I should be able to have access to all available part data for that bolt - including specifications, tolerances, 3D models, compatible mates, replacements - right at the parts cabinet. For now, this could be achievable by some user gesture at the parts cabinet (e.g. pressing a tactile switch at the individual part compartment) pushing a notification to a nearby iPad. As interaction hardware evolves, I would hope that this would happen within the parts organizer itself, through the use of haptic/gestural info (picking a part out of a bin) and integrated displays.
My purchasing system should know what parts I have on hand. When I order parts, it's almost exclusively through webstores. When I hit the "confirm your order" page, I want my inventory tracking software to scan for similar parts in my database and alert me if I've got anything in stock that would work for what I'm doing. If I'm ordering M4x12 button head cap screws and I have M4x12 socket head cap screws in stock, it's possible that I could save time, money, and inventory space by redesigning my assembly to accept what I have in stock. Conversely: When I place an order, my inventory system should know about it and prepare my parts organizer to accept new inventory.
Everything should have a 3D model. This is a bit of a pet peeve of mine. It blows my mind that many PCBs are designed without a digital visual check for interferences, and the situation is even crazier when you consider integrating PCBs into mechanical assemblies. I've spent a lot of time modeling off-the-shelf components for my own use, and have begun posting them on GrabCAD for others to use. It's my hope that this type of thing catches on, and that manufacturers find ways to support/help the effort.
No paper. My previous parts organizers relied heavily on sticky notes and Sharpies, as I suspect most contemporary systems do. This is absurd. What happens when you run through stock of a particular part, and decide not to reorder? Well, you spend ten minutes scraping a crusty old label off of the bin, or taping over it with a new one. Adhesives fail over time, and pen-and-paper just isn't modular enough for the rapid changes in direction that modern product development shops go through. My bins should be unlabeled. Instead, I'll identify parts by comparing them to their 3D models (viewable in my parts organizer's interactive display), or - better yet - by my parts organizer knowing what I'm doing (through whatever gestural interaction it uses) and telling me what I'm looking at.

What I've described here is huge, but not that conceptually complex. It also has the capacity to be expanded recursively, to apply to all kinds of physical and digital objects. A cohesive, consistent system for tracking and managing parts will allow for improvements in innovation and distribution techniques to reach their full potential. And I worry that without such a system, the benefits of rapid prototyping, just-in-time manufacturing, and distributed, adaptive supply chains will be highly constrained.