A few things...
He doesn't do any maintenance on the caliper when replacing the brake pads. As the pad wears down, more of the piston is exposed, and gets gunked up with road grime and brake dust. If you don't thoroughly clean the piston before pushing it back in, it can lead to seal problems. It's best to completely tear the caliper down and ensure everything is clean and functional, but at the very least you want to scrub the piston clean.
When he's putting it back together, he puts the caliper bracket on wrong. There's a groove in the caliper that fits over a tab on the swingarm to keep it from rotating. You basically have to slide the bracket in from the back of the bike. It's a whole lot simpler to do if you unbolt the caliper from the bracket. That gives you complete freedom to move the bracket around however you need while installing the axle, and you don't have to worry about lining up the disc while doing it. Once you've got the axle in, you can just drop the caliper over the disc and bolt it back to the bracket.
Also, once you've got the rear wheel out, it's only a few more bolts to completely remove the swingarm. That would allow you to install a pre-made chain loop if you prefer. It'll also get you into a few areas that tend to get ignored for cleaning and lubing. It's definitely not necessary, but it's not a ton of extra work if you've got a centerstand.
When aligning the wheel, the marks on the swingarm have been known to not be all that accurate. It's a good place to start and better than nothing, but it's best to align it with a more precise method.
