There are many ways to build a reactor but the main points need to be the same if one wants to avoid adding trouble. We can get away with modification if we understand the downside to some of the design changes we make. The video has a number of changes to the original design and we should understand what they can do to us. He kind of lost my interest when he went for using pliers on plastic! But in general the job can be more simple than his design.
Keep in mind that you will sacrifice flow when you add fittings or turns like elbows so it is good to avoid these if you want max filter function.
Adding fittings is one way to drive up the cost. Pipe is cheap while fittings are not. Reduced fittings means reduced cost and less loss of flow!
Water must enter at the top and flow down while CO2 bubbles are trying to float up against the stream. This is where the design has to be tailored to match the size of the water flow (GPH) of the filter as well as how much CO2 is expected to be added. Too much water flow through too short a length of pipe will let bubbles be blown out into the tank. Adding a fitting to put the Co2 into the side of the water flow is one way to lean toward getting a large bubble of CO2 at the top where it may create noise. Better to let the CO2 enter the water flow in the center of the stream where flow is at the max.
Whether you have the water enter through tubing pulled through an undersized hole to release the CO2 in the center or use a fitting takes a bit of looking at how you think. If you trust the original Grigg's design, you pull it in through the hole. But if it makes you worry to not use a fitting, you have to know it may create noise. Just make an informed tradeoff? Reduced flow and possible noise or trust, that is your choice.
On putting the PVC together, there are choices as well. I use very few parts and certainly do not use extra threaded fittings to put the two ends together. I can't see any reason to ever want to unscrew them so why add complexity? I can cut it if I ever need to get inside.
Glueing up the parts also has a few details that I do differently. Part of the question of how to do it depends on the materials. If you are using old crusty PVC that has a layer of oxidation, the primer is needed, but then he also skipped over one point that I consider important. One way to avoid the primer and still get a better job is to use sandpaper. When pipe is cut, it will often have burrs at the cut ends and those need to be smoothed out by sanding. At the same time , it is often recommended to roll the pipe around in the sandpaper to remove dirt and oxidation as well as give the pipe and fittings some "tooth" to make the solvent work better. scrub the inside of the fittings as well. Also it is wise to test the fit of the pipe in the fittings before going to the solvent. If you add solvent and then find there is a burr on the pipe so that it won't fit---you get to go shopping for more parts!
If you use sandpaper to remove the corrosion and make things fit better, you don't need the ugly purple!
If you ever pour a jug of the purple out on good stuff, you will know why it is good to avoid it. Sandpaper has never cost me a new pair of pants, socks, and shoes!