These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: Twilight Struggle
Complacent Gaming Syndrome: The vast majority of games will see the Soviet player coup Iran on his first action round of the first turn - with a strong card or a decent roll of the die it at least eliminates easy US access to South Asia, as well as take care of military operations requirements early for the Soviets. Similarly, in games where handicaps are used, most times the US is given an extra influence at the start, and most of those times the US player uses that influence in Iran to shore it up.
Game Breaker: There are some cards in this game that get accused of this. Here are the worst offenders:
Aldrich Ames, Late War Soviet event. This card lets the Soviet player look at the US hand and then dictate the order the US has to play his cards in. What makes this even more powerful is that there are some cards that, if the US plays them, will trigger global nuclear war. Normally the US can either hold them over to next turn, or play them at a time when they will not end the world. But, if the US is holding one of them and gets hit by Ames, they lose the game, no questions asked. Ames is so deadly, the designers nerfed him in the Deluxe edition; he was the only card that got this treatment.
Red Scare/Purge, Early War, playable by either side. The effect is to subtract 1 from all your opponent's cards ops value (for example, 2's become 1's) for the rest of the turn. This is very, very strong, especially against the US during the Early War. If the same player draws this card twice in the Early War it can decide the game, although not always.
NORAD, Early War US event, expansion card in the deluxe edition. It is usually in the Soviet interest to maintain DEFCON at 2 as much as possible - since they go first in on-board action it gives the Soviets free reign to coup a battleground (prior to every turn DEFCON improves by one, thus when the Soviets coup it goes down to two and prevents the US from couping it backnote Unless "Nuclear Subs" is in play) and also lock down the Middle East, which the US often has a difficult time with, especially in the early game. NORAD gives the US one free influence anywhere there is already US influence when DEFCON falls to 2 during the action phase, thus serving to negate the Soviet advantage to some extent.
That One Rule: Amongst players learning the game, the rules of realignment tend to be the most misunderstood, partially because it's not used a lot, especially in the Early War.
Unconventional Learning Experience : You will learn a LOT about the Cold War in this game. It certainly helps that the scenario guide has a section that explains the real-life historical context of every card.