My loose talk generated a question on the difference between 'fundamentally flawed' vs 'broken'.
They are fairly similar, but not interchangeable. In my mind, "Broken" means that a game has a single, dominant strategy (usually a very obvious, very easy to implement one). It usually applies to Asymmetric games, or CCGs (where players have their own resource set), or any game that somehow differentiates the players (otherwise they could all follow the broken strategy). If it suddenly turned out that you could win a chess game (by move two or three) by 1. H3!, Chess would become broken. No fun to play (at least, no fun to play if 1. H3! was the opening).
I mainly fling "Broken" around in relation to CCGs. I don't just play Shadowfist, I playtest it. Our job is to make sure that no published card dominates the game. Our other job is to try to make all published cards good enough to be playable, and to make them interesting.
"Flawed" means that the game has a problem. This is much more subjective (I think). Power Grid may be flawed, but I still play it. "Fundamentally flawed" just extends that. The core of the game is flawed, not just some peripheral system.
To a certain extant, flaws depend on what you are trying to do. If I try to write a tragic play, jokes are a flaw. If you view Taj Mahal as a poker variant, then it's structure is clearly flawed. [Sklansky and Malmouth discuss how ante structures affect the game and how some are better than others, in case you are interested.] By Greg's summary (which I prefer to my poker analogy), the same idea comes out. There is a clear way to win (not get involved in fights), which you have no control over. Since a game (by my hazy definition) must give you some control over it (otherwise it would be a simulation, or something), Taj Mahal is flawed. The fundamental system doesn't work. But it's not broken. There's no dominant path to victory.
Broken, in my mind, is proveable. If I claim card X is broken in Shadowfist, I should be able to build a deck that can 'run the table' against any other deck that doesn't have the same card (or possibly a card that specifically cancels mine). [In fact, I have been arguing that a card on the list for next set may be broken, and trying to build such a deck]. Similarly, if I claim that the "Road Strategy" in Settlers is broken, I should be able to win if I follow the strategy against opponents that don't. If the "H3" opening is broken, I can defeat all comers (as white).
Flawed depends on what you set out to do. A game that sets out to be a quick, fluffy romp is flawed if the rules take two hours to explain. Paths of Glory's rules take forever to read, but it's not flawed (or, if it is, not for that reason). A game that sets out to model historical events that produces wildly impossible results would be flawed. Imagine a WWII game where the US could force a Japanese surrender in Feb '42 after Pearl Harbor. [Perhaps 'inaccurate' would be better, but that's just a specific flaw].
Of course, flaws have levels. Mild flaws are just that, mild. Lots of games have the flaw that a weak player can throw a game (as discussed before). The game may be interesting in general, even if a particular playing isn't. As you expand the flaw (so that random events, or unknowable distributions decide the game), then it becomes a major flaw.
Sometimes I just don't like a game. I don't want to play 60 hour games that extensively covers the some minor war, or fluffy silly games. But if those games set out to do that, I can't call them flawed. Taj Mahal sets out to be a "Reiner Knizia" game in the Alea box line. That gives me certain expectations about how much control players should have. The core system of the game (as I've tried to describe with my analogy) puts the players in an uncontrollable situation. Take Greg's formulation:
You win the game by avoiding fights. You have virtually no control over whether you get into a fight or not.
If that assessment is true, then 'fundamentally flawed' strikes me as perfect description. [Needless to say, I agree with the assessment, and many commentors disagree].
By the way: I'm done referring to Greg's formulation, as I may start owing him royalties.
Update: I just played a few games of Roll or Don't versus my computer. Here randomness isn't a flaw, as I expect that in a 'push your luck' style of game.