Decomposing something into 'molecules' is immediately indicative of a non-chemistry background! To try to address your question a bit more directly, I can see a couple of ways of looking at the thought experiment:
1) It decomposes everything to simplest possible component stable molecular structures.
In the case of organic material, plastics etc, you will probably end up with a preponderance of various gases and water, as largely this disassembly is equivalent to complete combustion (CO₂, H₂O, NH₃) likely being the main resulting candidates. These would float out into the atmosphere unless captured.
In the case of inorganic material, e.g. a computer motherboard you will end up with many molecules of various metals, most of which would rapidly oxidise due to their very high surface area (being unimolecular), and various silicates and ceramic unit cells. All of these would be incredibly fine aerosols or dissolved in atmospheric water, similarly rapidly dispersing unless contained.
Results would likely include enhancing the greenhouse effect (on balance as some compounds will diminish it), inducing acid rain (sulfates, nitrates), causing algal blooms/biome damage.
If you had storage for different outputs then you would be producing several industrially useful compounds and if you partnered it with metal reclamation facilities to deal with all the metal oxides it might be a useful way of recycling, energy no object.
2) It decomposes and sorts everything by chemical element.
Assuming you have a nice little storage container for each element (reasonable given you are sorting into the simplest molecule of a pure element), you would end up with various cylinders of oxygen, hydrogen, nitrogen, lumps of metal, lumps/powders of inorganic materials like phosphorus, sulfur, silicon. This would be potentially useful, but incredibly energetically expensive even beyond the separation system outlined by Uncle Al, so would be considerable only in the case of having essentially limitless free energy (many nuclear fusion plants/orbital solar collectors/dyson sphere type energy availability I suspect).
Issues here would relate to various elements being highly reactive on contact with air (or rather the oxygen/water in it). Obvious examples include allotropes of phosphorus and the rare earth metals.
Other issues unaddressed include fractional distillation and cracking of small molecule gases into smallest molecule gases, how to prevent reaction inside the vessel i.e. actually separate things rather than just provide them with huge amounts of energy to react with each other etc