Dieter: Many amateurs, in particular Western amateurs, neglect the very basic principle of cutting and connecting, because they are somehow overly confident in the living potential of their stones, underestimating the effect over time of forces being spread. They overvalue the development of areas, putting new stones in large empty spaces, and undervalue the stability of existing groups, omitting extra stones in occupied areas to reinforce them.
For a long time I have thought this is due to the way in which Go is explained to beginners, as a game where empty points need to be surrounded (and not a game where as much living stones need to be put on the board). But in the West, we've taken the "territory way" from the Japanese. So if there were a fundamental problem due to the explanation of the rules, then the Japanese would suffer as much from it as Westerners do. Which is not the case, I believe ...
Lately I have been thinking there is a deeper cultural reason for neglecting the cut & connect principle. Let's assume Western society has been based on farming, where ownership of land prevails, and Eastern society has been based on trade, where social cohesion prevails. Maybe Western people have a spatially more developed brain, easily constructing imaginary rectangles as "territory" and assigning ownership to those rectangles. Maybe Eastern people have a socially more developed brain, easily dissociating groups of stones and seeing the way they cooperate. Maybe they have an inner sense, seeing "territory" as a safe harbour for potential stones, offered by strong groups of existing stones.
Therefore, Western amateurs go about mapping out territories, invading opponent maps by envy, while Eastern players reinforce group structures, and see an invasion as undermining the opponent group structure.
Herman: I think that the assertion "in particular Western amateurs" in the first sentence of the second section is dubious. Although the Japanese have a reputation for "solid play", I think this is biased because mostly we only see professional level games here. Many of the Japanese amateurs I have played against on European go congresses were fierce fighters, with the same tendency to unreasonable optimism about their weak groups that western amateurs have.
I think the neglect of connecting is a general feature of weaker players, and I think it is not because territory is explained as the goal of the game, but because territory is one of the most basic and successful strategies there is.
Weak players (say DDK) have a horrible tendency to always connect stones in atari, and to always capture stones when they get a chance, no matter how important or unimportant those stones are. This, in my view, is because the "always save my own stones, always capture his stones" strategy is a very good one. Do those two basic things consistently, and you'll probably soar from 30 kyu to 20 kyu. That's ten whole grades! The fact that you will now need to 'refine'' that strategy, that you need to differentiate between "important stones" and "unimportant stones" is irrelevant at that level. Learning to make that distinction is important, sure, but it is hard, and you'll only crawl up the ranks slowly as you get better and better at it.
Another very successful strategy, and another favorite of the weaker player, is the "always attack, even when you can't attack, then still attack!" way of playing. As a strategy, it gains you some strength very quickly, because attacking is very often the right thing to do. Whereas that whole learning "when to attack, when to defend and when to take territory" thing is hard, and slow going.
Focusing on surrounding territory is yet another one of those successful strategies. And then, again, you'll need to learn when to take territory and when to defend your weak groups. So I think it is, and will always be, the domain of the weaker player to focus to much on one such issue, and only later to learn restraint and sublety :-)
Dieter: That's what you get when the Japanese westernize ... #:-7. OK, so my explanation was too far fetched. Still I think the cut & connect neglection is more fundamental than the rest of the issues, which indeed balance out towards mastery.
tapir: +1 to Herman. (I understand that there is some fun in speculative explanations of cultural differences, regardless of whether the difference in question exists or whether the explanation holds any water. But why would you concede trade as an Eastern preoccupation while living in Flanders? Well, at least a Dutch player disagreed :))
Timm: I also agree with Herman. One reason for which amateurs could possibly have that tendency to leave weaknesses is that it is harder to attack effectively, or to kill, than to play in empty areas or live. So you don't get punished for overplaying. Also playing thick is actually playing slow if you can't use the thickness efficiently enough, so it's easy to keep on playing too fast.