The best way to decide whether the problem has been solved is clearly to first unravel what we mean by the term solved. The two most important factors in my opinion have got to be the scenario and and the accuracy, which I've picked apart below.
The most compelling scenarios are the ones in which the software does as much of the hard work as possible, allowing the hardware to remain simple and inexpensive. Furthermore, the installation process should also be free from any dedicated training phase in which the temporary control of appliances is required or additional monitoring equipment is deployed. This style of approach clearly affords the maximum scalability, which is essential if disaggregated data is ever to reach the masses. While approaches are still being proposed that don't address this scenario, there's still quite a way to go yet.
It's very easy to get carried away when reading papers how one approach has achieved X% accuracy, while another achieved Y% accuracy. However, I'm fairly sure that aiming for 100% disaggregation accuracy is not only unrealistic, but also unnecessary too. I think it's far more important that energy disaggregation is used as a platform from which personalised, actionable, energy-saving suggestions can be derived. Therefore, disaggregation only needs to be accurate enough to convincingly determine the bigger picture, and any effort beyond this is likely to be a waste of time.
On a final note, even if there exists an approach that's managed to address the above scenario to a suitable level of accuracy, this is still only only piece of the disaggregation puzzle. The diversity of electricity consumption means that different countries and buildings require different approaches, and there will always be a niche sub-area of disaggregation just waiting to be found.