did you actually WATCH the top video that you linked (@1:55)? This demonstrates pretty conclusively that the spread method traps air. It may not directly say that this is bad, but it is

I guess also worth pointing out (that a couple commenters to that video missed) that the acrylic thing he was putting down was meant to simulate a heatsink. He wasn't advocating spreading it with that, removing it, then attaching your heatsink. Basically the video guy's point was a) spread method is awful b) make sure you use enough compound and c) don't use too much compound. Multiple dots, lines, globs, smiley faces...whatever - they don't matter.
Also, look at the comments to video 2. Look at how the video has received more thumbs down than up (not that the masses are always right, but if youtube viewers think something is awful, typically it is). Note the second-highest rated comment. Also, WTF is the point of making a pretty shape if you're just going to spread it everywhere manually anyway?
You challenge us to look at your pictures and ask us to let you know if we see anything wrong with the coverage you have. The point is we can't. You've already removed the heatsink and things never seperate evenly. We can't see where the air bubbles were. You point out that with the dot method, the corners are sometimes not covered - this is a good point and likely leads to sub-optimal heat transfer. However, the chip manufacturers as well as the thermal compound makers will tell you that MOST of the heat comes out the center region (because that's where most of the processing occurs). Additionally, many heatsinks have a round base that is slightly smaller than the square chip anyway, so it doesn't matter if those corners are uncovered, in fact it will help A BIT if they are uncovered (heat transfer from the HS to air vs HS to TIM to air). Of course, if you had a square base or circumscribe the chip with the base of the heatsink, it'd be better to go out all the way to the edges, but that's where the line or cross methods come in handy.
I'm actually concerned with the apply-pressure methods (dots, lines, etc) as well, because I figure if I initially apply pressure a bit more on the left side, it'll squirt the stuff to the right, not leaving much to spread to the left. I assume the high viscosity of modern pastes corrects for this a bit, which is why manufactures (of chips, heatsinks and pastes) don't really mention it, other than to suggest that you apply diagonal pressure. In any case, a spread method is undesirable, so your best bet is learning the proper technique of applying equal pressure and application of an ideal amount of TIM with a dot/line method.