I don't find a prompter needed to do videos. At best, I make some notes in the style of powerpoint slideshows (or bullet point lists) to make sure I don't forget to mention something or to stop me from going off topic.
As a critique in general, at the start the brightness was a bit low so the camera messed up the colors. For the future, consider turning on a lamp in the back of the camera and raising the camera a bit so that it shoots the desk at a small angle - stack some books or something to reach the height, if you don't have a tripod.
Be a bit more careful about where the camera focuses .. at the start, the camera couldn't focus on the red digits because the unit was too close to it ... also it couldn't focus on the iron tip and handle because of the stuff in the back - in such cases, put your palm behind the tip or what you want to go in focus, or grab a sheet of white paper and put it behind what you want focused.
Another minor annoyance would be that there's no normalizing on the audio, when you get close to the camera your voice is louder and so on. This can be fixed at editing or (the easier way) using a lavalier microphone that you put on your shirt so that it's always at the same distance from your mouth.
Some observations...
When you try to melt the first joint... you put solder on the tip and then you rub it on the yellow sponge (from what I can tell based on the sound)... this is actually a wrong technique. You put a very small amount of solder on the tip, you clean that off using the steel wool thing or using chemwhipes (if you don't have either, just some paper towels/handkerchiefs will work) and remove the big chunks of oxidized solder and crap that's on the iron from the last operation.
Then you rub it on the wet sponge to remove the small amounts of oxides that still are on the iron.. you don't want to get your sponge dirty with all the oxidized solder.
You add a thin layer of solder to the tip and when you put the iron tip on the joint you want to melt, you may want to add a bit of solder right at the point where the iron meets the joint, so that heat from your iron will transfer faster to the joint.
You then considered some traces as ground trace and more difficult to desolder but in reality it looks like it's much "lighter" trace. The last examples can actually be considered as joints harder to desolder at that 550f temperature.
Also it would be worth pointing out that in lots of cases where you have to do what you did in the video, adding a drop of liquid flux helps a lot, because when you add heat from the iron, the oxides on the surface on the pcb and joint will be attacked by the flux and will make heat transfer easier. This is what actually happens (but not that well) when you add solder to the point where the iron touches the joint: the flux in the middle of the wire attacks the joint a bit before the actual solder melts and helps the iron transfer heat.
See these two videos as a refresher on soldering basics:
(skip the first minute, we now use isopropyl alcholol and liquid fluxes, no need to rub the leads anymore to break the oxides)
(this a bit paranoid, but it's worth watching how he uses the soldering iron, cleaning the tip then using the sponge) .. alcohol he uses is plain isopropyl alcohol.