Hi Martin,
Long time Youtube subscriber and commenter on your videos, finally gave in and decided to make an account

I want to post some Youtube videos that I found to be very informative in regards to soldering because I saw in your last video that comment about the Radioshack solder being lead free (it's not) and that the other solder was bad (which theoretically shouldn't be - 63/37 mix in general is better than 60/40 - but it was probably lacking in the flux department, if it had any)
As I said in my last comment, I would suggest avoiding Radioshack (they're no better than eBay Chinese sellers imho) and buying a quality solder wire from Digikey.com or Newark.com or Mouser.com (reputable US online sellers) and some good no-clean flux pen. I'm using a Multicore 0.56mm diameter 63/37 solder with 2-3% no-clean flux in it, it works great with the Hakko 936 I have.
With such a quality iron like that Hakko FX888 you have, you would be impressed with the quality of soldering with such good quality solder.
Anyway, here's the videos I mentioned
Pace Worldwide has posted a whole series of videos they used for training, courses etc. While they're old, the information still applies and it's very good. Here's the first video in the series:
Basic Soldering Lesson 1 - "Solder & Flux"
http://www.youtube.com/watch?v=vIT4ra6Mo0sThe other videos in the series should be visible on the sidebar or otherwise easy to find.. they show how to use flux, how to solder wires, through hole parts etc
I'm going to give a special mention to :
Basic Soldering Lesson 6 - "Component Soldering"
http://www.youtube.com/watch?v=AY5M-lGxvzobut really, all videos in the series are very informative and relatively short so they're worth watching.
Besides this Pace series, there's also a teacher that posted a series of videos with soldering for avionics, based on Nasa textbooks. The soldering he does is a bit over the board, paranoic even, with lot of cleaning of wires and solder tip, but I found the videos very good to learn the technique to tin wires and solder wires together
Tinning a wire by hand :
http://www.youtube.com/watch?v=0SnOW2VdCTIor with a solder pot :
http://www.youtube.com/watch?v=BiVkI4IooH4splicing two wires with solder (this is how you probably should have soldered the mains wires if you had no choice but to do it instead of replacing cable):
http://www.youtube.com/watch?v=xPkc6k5uWUQthrough hole soldering paranoic level:
http://www.youtube.com/watch?v=Vynb_HdEIDU--
Dave also has some quite good soldering lessons, here's part 1.. the other 2 are next in series, easily found:
http://www.youtube.com/watch?v=J5Sb21qbpEQ