Are there any?

Negative aspects of the HC³ process are astonishingly minimal.
One is it's voracious appetite. We have found in many instances that the client does not possess enough feedstock to keep the facility running 24 hours a day, a prime requirement of their operation.

No Gasoline

One may not even consider a downside is the restriction to diesel fuel and jet-fuel. While it is actually possible to produce gasoline with this process, it is far less effective from an energy yield and cost point of view. There is a 10% drop from diesel to jet-fuel; the yield iis lower than that of diesel fuel.

On the other hand, with a heavy truck population of about 5 million diesel trucks in the US, 400,000 rigs in California alone, not counting construction machinery, forklifts or diesel locomotives, and with a diesel fuel consumption of 4 million barrels per day (!), we will need years just to satisfy the ravenous demand for diesel fuel.

There will be no lack of customers for decades.

Again, this is not really a downside but only a logical result. In actuality, HC³ can only convert what is contained in the raw waste material, and not everything can be converted 100% into diesel. While the largest part of the byproduct is distilled (albeit extremely clean) water, which can be safely disposed of such as through irrigation, etc., there is a variety of other byproducts.

Most of them are base material good for the chemical industry, which could result in additional income. For example, the toxic, poisonous chlorine in PVC and PCB (transformer oils) is converted into potassium chlorate, a crystalline compound ostensibly used as an oxidizing agent, a bleach, and a disinfectant. It is also widely used for the manufacture of safety matches and fireworks.

Some raw materials (e.g. coal) result in carbon pellets as a byproduct, which can be sold at a premium price as a base material for carbon fibers.

In any case, the amount of byproducts is the least among all alternative fuels.

It does seem too good to be true but Edison heard the same when he proposed running wires thru everybody's house that would flood it with light (and TVs and computers and blenders and microwaves, et al).

Imagine the skepticism the Wright Brothers met when they scheduled regular 500 person flights to Paris . . . off-season!