Warden Kuril, the head honcho of the Purgatory prison ship, welcomes Shepard and two other armed companions (who are any of the following a high ranking operative for one of the most powerful terrorist organizations in the galaxy; a seasoned lieutenant to same; a mercenary renowned for his ruthlessness and extremely high salary; a former C-Sec Officer and one time Spectre candidate who single-handedly held off three of the most ruthless mercenary groups in the galaxy in the heart of the Terminus Systems (INCLUDING the same mercenary group Warden Kuril is a part of), on a station renowned for being the galaxy's Wretched Hive for three days with just a sniper rifle; a master thief so adept at her craft that no one recognises her hacking an advertisement terminal in a public space in broad daylight, or speaking to a woman/man who is both thought dead and renowned as a legendary figure for stopping Saren and the Geth; a scientist who killed people with farming equipment and participated in mass population control experiments; and a genetically engineered member of a race of Blood Knights previously under the care of a big shot warlord) on board with aims to kidnap them and sell them off to slavers. You'd Expect: that Kuril would require Shepard and his/her companions to disarm, in accordance with standard security procedures for guests aboard prison ships, and to refuse them entry if they do not comply. Or, failing that, that Kuril would scrap the whole "kidnap and sell" plan if unable to force Shepard and company to disarm. Instead: Although Kuril does make an attempt at requiring the party to disarm, when Shepard refuses to do so, he lets them proceed fully armed (including, possibly, with TACTICAL NUCLEAR WEAPONS) and then attempts to capture them near a security checkpoint. This works about as well as you'd expect. Also: He tells Shep and the party what he's up to seconds before they step into a room that would incapacitate all of them. If he had waited another 30 seconds, he would've had all of them safely captured.
Another example, this one on part of the player. Late in the game, and assuming he/she took the necessary steps to recruit Morinth, she will invite Shepard over to meld with each other. Morinth is a sociopathicArdat-Yakshi and Serial Killer with the ability to control people's minds, an ability Shepard resisted in the past to betray Samara, Morinth's mother. Morinth claims that Shepard's Heroic Willpower will enable him/her to survive the process, despite the fact nobody in recorded history has ever survived an Ardat-Yakshi's melding. You'd Expect: Shepard to decline the offer, what with the imminent war against the Reapers putting enough of a threat to his/her health. Instead: Shepard can choose to meld with Morinth, resulting in a Non Standard Game Over. In his/her defense, this one is completely on you.
And again in Mass Effect 2, in Jacob's Loyalty Mission you discover that his father had deliberately not activated a distress beacon while on a deserted planet and instead had turned the crew into his slaves via local food that was mentally damaging them. You'd Expect: Him to realize that sooner or later his supplies of clean food would eventually run out and he would have to activate that distress beacon so he should make sure that his slaves aren't holding on to anything that would incriminate him. At the very least you would expect him to realize this when his food does run out and he activates the distress beacon. Instead: He not only left untouched a series of log entries at his crashed shipnote that, while suspicious, didn't directly incriminate him he permitted one of his slaves to keep a record that directly stated that he had enslaved them and murdered any officers who got in his way. When a rescue team in the form of Shepard arrives he doesn't even bother to try to come up with a good lie.
Kai Leng's special ability seems to be channeling Idiot Balls, since everyone who goes near him starts acting in ways that often seem stupid:
Overview: Shepard and his squad are en route via aircar to intercept Cerberus as they move towards the Council members, when Kai Leng suddenly jumps on the roof of their car. You'd Expect: Shepard to start swerving the car to attempt to send Kai Leng flying, or make him smack into one of the many underpasses that the car is flying past, and at least heavily weaken his Deflector Shields as he uses them to hang onto the vehicle. Instead: Shepard opens the door and starts shooting with a Predator pistols/he probably wasn't even carrying, Kai Leng then sabotages their car and causes them to crash, allowing Cerberus to get a head start on the race to the Council.
Leng himself is equally vulnerable to them at times. Overview: Kai Leng is attacking the salarian Councillor, when suddenly Thane Krios jumps out of nowhere. You'd Expect: Kai Leng to simply hide and stab Thane followed by the Councillor before fleeing Shepard and his/her squad. Or, failing that, at least activate his Deflector Shields to deflect Thane's biotic and melee attacks and any possible crossfire from Team Shepard should Thane move out of friendly fire range. Instead: Kai Leng decides to get embroiled in a stand-up fight with the sick drell, buying the Councillor time to escape, and costing Cerberus their objective.
An in-universe example pops up with the Geth Consensus when they are attacked by the quarian Migrant Fleet. Overview: The Geth Consensus is attacked by the Migrant Fleet, which destroys the Dyson Sphere they were building around Rannoch, and their territory is being overrun quickly. The destruction of the Dyson Sphere deletes the majority of the geth "species" and thus reduces their collective cognitive ability. You'd Expect: The geth to call for assistance from Shepard to prevent the quarians from overunning them. Instead: Following their emergency survival protocols, the geth seek out immediate assistance from the Reapers, who give them upgrades to their coding to render them immune to the quarians' weapons, at the expense of being enslaved or exterminated by the Reapers once their usefulness runs out. If Shepard points out that the geth made a rather poor long-term decision, Legion agrees with that assessment.
The quarian Migrant Fleet, in turn, makes its own equally stupid but justified in-universe decision in attacking the geth. You'd Expect: The quarians, aware of the Reaper threat, to direct their military buildup to counter the Reapers, instead of launching into a destructive and costly war with the geth. Instead: The quarians, sensing a chance to completely destroy their old enemy and recover their homeworld, launch an attack with the new weapons that render the geth helpless. While initially successful, the quarians damage the geth's overall cognitive ability, and the greatly reduced Geth Consensus turns to the Reapers for immediate help. The upgraded geth trap the Migrant Fleet inside the Rannoch mass relay so they can't escape, and even if Shepard brokers a peace between them, the damage both sides suffered in the war reduces their ability to fight the Reapers.
The Citadel DLC: A villainous impostor pretending to be Shepard has just seized control of the Normandy with a squad of mercenaries. You'd Expect: They would kill all witnesses, ensuring that nobody could report the people inexplicably wearing CAT-6 armour accompanying Shepard, thereby easing the identity theft. Instead: The villain just fires Traynor and kicks her off the ship, allowing Traynor to aid the real Shepard in regaining access to the Normandy before it can leave.