The colonists in "The Power of the Daleks". Daleks have conquered the Earth twice! Now there are three on a derelict ship. You'd Expect: The colonists would read their history and act accordingly. Even if we accept that the story is set before "The Daleks' Master Plan" and ignore the invasions in "Doomsday" and "The Stolen Earth"/"Journey's End" (which weren't written for another four decades), you'd think they'd at least remember the Dalek invasion of Earth in the story called "The Dalek Invasion of Earth". Instead: They accept these supposed servants at face value. This leads directly to the Daleks manufacturing dozens more, and exterminating around half of the colonists.
In "The Sea Devils", the Royal Navy has rescued both The Doctor and The Master from their watery prison just in time, and have The Master under guard in a hovercraft. You'd Expect: The Royal Navy to keep a massive armed guard on The Master, ready to fill him full of lead whether The Doctor likes it or not. And, The Doctor might warn them about his mastery of disguise. Oh, and you think the crew of the hovercraft might keep an accurate count of their own members. AND, if that weren't enough, that they would always make sure more than one person is guarding a piece of military equipment on the order of a hovercraft. Instead: The Master is apparently left by himself with one sailor to guard him on a small hovercraft. He somehow has time to hypnotize the salor, place a Perfect Latex Disguise on him and palm him off as The Master's own corpse. Then, as The Doctor and the Royal Navy troops are gawking at the reveal, The Master makes off with the hovercraft. This was the serial that the Royal Navy chose, out of all Doctor Who, to endorse and lend the BBC resources for.
In "Invasion of the Dinosaurs" episode 3, Sarah Jane decides to take pictures of a chained, sedated Tyrannosaurus Rex. You'd Expect: Her to keep pictures to a minimum, not use flashes or anything that could annoy the dinosaur, and keep to the small antechamber of the main hanger where the dinosaur is held. Instead: She jams on that flash hard as hell, and even when the dinosaur stirs, she just waltzes in to take close-ups, naturally awakening the dinosaur, which breaks the chains, because The Mole has tampered with them. She's hit by a falling 2x4 while screamingly trying to open the exit door, which has been locked by The Mole, as the dinosaur bashes the anteroom with its tail. Thankfully, Sarah Jane's Character Development moves her far away from these hapless moments as she gets older.
"Genesis of the Daleks": Gharman, one of the scientists not falling in line with Davros, starts raising concerns about his plans for the Daleks, out loud, and starts formulating a rebellion. Later on, he meets with Nyder, Davros's unflinchingly loyal dragon, who claims he's disgusted by Davros' perversions of science. You'd Expect: Gharman would realise there's no way in Hell Nyder would turn on Davros now, after everything else he's done. Instead: Gharman tells Nyder everything. The minute Nyder's got what he needs, he bludgeons Gharman unconscious and hands him to Davros, who plans to lobotomise Gharman.
Making it worse: Gharman escapes due to help, and forms a rebellion against Davros. It successfully manages to overthrow Davros. You'd Expect: For them to kill Davros, or lock him up, just get rid of him and not let him do anything, after what happened the last time Davros talked someone into giving him a chance. Anything, anything but what they do. Instead: Gharman allows Davros to speak to his accusers, which A) gives Davros the chance to turn some of them back to his side, and B) allows the Daleks time to arrive. Three guesses what happens next.
At the end of "The Deadly Assassin", after the Doctor leaves in his TARDIS, the two Time Lords he has befriended witness the Master closing the door to his own TARDIS, proving that he isn't so dead after all. You'd Expect: them to at least try to apprehend the Master — if not directly, then by informing the proper authorities. Even if they didn't succeed in getting him, at least they made an effort. Instead: not only do they do nothing, they take the time to speculate whether the Doctor will ever encounter the Master again, as the villain escapes right in front of them.
In "Warriors of the Deep", one of the story's main villains encounters the dangerous Myrka. You'd Expect: her to try and escape from the Myrka and come up with a clever way to defeat him (or at least rely on someone else to defeat him). Instead: She tries to fight him with her martial art skills. Guess what happens to her.
During his debut in "The Twin Dilemma", the Sixth Doctor unsuccessfully tries to kill the story's Big Bad, Mestor, who in announces that he intends to possess the Doctor's body and absorb his mind. The Doctor's former tutor, Azmael tries to warn him that this would be easy for Mestor considering the Doctor's mind is still screwed up from his recent regeneration, but the Doctor brushes off the warning and actually demands that Mestor try to possess him. You'd Expect: Mestor to just get on with it and possess the Doctor, who is quite literally asking for it. Instead: He possesses Azmael, just to be a Jerkass and attempt to intimidate the Doctor prior to taking him over. Azmael, by the way, is a vastly experienced Time Lord who isn't suffering post-regenerative trauma. Result: the Doctor successfully destroys Mestor's body, and then Azmael retakes control of his own body and commits suicide, taking Mestor with him.
The Seventh Doctor is knocked out and given an amnesia drug by the Rani, a rogue Time Lord who has battled the Doctor at least once before. He eventually wakes up, and she disguises herself as his companion Mel and tells him that he's in his laboratory (actually the Rani's). Moments later however, the Doctor finds a gun that he actually says out loud is powerful enough to blast any passing spaceship out of orbit and — unbeknownst to him — shot the TARDIS down so violently it caused him to regenerate.note (At least, that was the intended explanation when the story was first broadcast. It was later retconned. Three times) You'd Expect: The Doctor to immediately realize that there's no reason why he'd have such a deadly weapon at all, to say nothing of leaving it just laying around in his "lab," and that something's obviously wrong. Insted: He just tosses it aside and never even looks at or mentions it again.
Later on, the real Mel happens by the lab, and the Doctor realizes that the "Mel" he's been dealing with unti this point is actually the Rani. He also meets two of the planet's natives, one of whom has been forced into reluctantly collaborating with the Rani, but the other of whom is actively opposing her. The Doctor realizes that the Rani will soon be returning to the lab. You'd Expect: The Doctor to have Mel and at least the rebellious alien (even if the other one doesn't want to co-operate) hide somewhere, then ambush and capture the Rani when she walks in. Instead: He just sends them all out, then assists the Rani in repairing a machine which she's been adamantly demanding that he fix while refusing to explain what it actually does, and then just stands around like a lemon as she drops her guise as Mel and activates the machine.
Rose in "The Empty Child". A rope swings in front of her in WWII London and she holds onto it. Then it starts moving away. You'd Expect: She would let go of it. Instead: She holds onto it as it pulls her of the roof and is left dangling from a great height.
In "The Girl in the Fireplace", at the end, the Doctor wants Reinette to come with him. However, the time window into her time forces her to take "the slow path" to his next visit. You'd Expect: He'd either bring her through the time window to avoid the problem, or he would use the TARDIS to get her. Instead: He tells her she has two minutes. Two minutes later, he goes back through the time window, but it's been several years in her time, and she's dead by the time he shows up.
In "The Satan Pit", the Beast reveals the darkest secrets of the people trapped in the mining facility. This greatly concerns them, and they demand the Doctor explain how the Beast could have known those things. You'd Expect: The Doctor to point out that many alien species, including the Ood and himself, have some form of telepathic communication, and the Beast is just reading their minds. The story is set far enough in the future that it wouldn't just be laughed off by the humans. Instead: The Doctor offers the lame excuse of 'what makes him right and not me?' which completely fails to convince the group and calm their nerves.
In "Evolution of the Daleks", two Daleks take a platoon of Dalek-controlled humans to destroy the Doctor. When the time comes to actually do so however, it's revealed that the Dalek's control of the humans is a bit faulty, and the humans promptly turn on their masters. You'd Expect: The Dalek commander (who was remotely monitoring the situation) to immediately realise that the humans are out of their control, and activate the self-termination devices placed in their bodies as a precaution. Once that's done, the Daleks accompanying them can exterminate the Doctor themselves. Instead: The humans are allowed to carry on shooting at the Daleks for a full minute, and succeed in destroying both of them. It's only after their destruction that the Dalek commander decides to terminate the humans.
Davros criticizes the Doctor for letting people around him die on his behalf, accusing him of turning people into weapons and even comparing it to his own creation of the Daleks. You'd Expect: The Doctor would laugh at Davros's ridiculous logic, pointing out that he's never told anyone to commit suicide for him and all those people acted of their own free will, whereas Davros created the Daleks specifically to kill people and is currently planning to wipe out the entire Universe. Instead: The Doctor believes every word and is convinced that he truly is a monster for just trying to do the right thing.
Rassilon arrives on Earth via a temporal link set up by the Master, which will soon bring the Time Lord homeworld Gallifrey back into existence. The Doctor doesn't want to let this happen, and threatens to shoot Rassilon with a revolver. Rassilon holds off on doing anything, and then the Doctor wheels around and points his gun at the Master, the death of whom would also prevent Rassilon's plan from working. You'd Expect: Rassilon to take full advantage of the Doctor's back being turned, and to blow the Doctor into his component atoms (which we'd seen Rassilon do to a rebellious Time Lady earlier in the episode). Instead: Rassilon just stands around and does nothing, eventually giving the Doctor time to Take a Third Option and disrupt Rassilon's plan without killing either him or the Master.
Rassilon still has the advantage and it's only a matter of time until his plan succeeds as long as he keeps the Master alive and on side. The Master is somewhat miffed that his own plans have blown up in his face, but is nonetheless willing to join Rassilon and the Time Lords in their ascension. You'd Expect: Rassilon to humor the Master and tell him what he wants to hear long enough for him to keep the Doctor from foiling his plan and then dispose of him when convenient. Instead: Rassilon immediately rejects the Master, saying "You're diseased!" and explaining how he could never join them. This infuriates the Master, who attacks Rassilon and provides the Doctor with the distraction he needs.
The Doctor and the group he's stuck with have managed to capture a member of the reptilian race, the Silurians, that have abducted several humans. He wants to use the Silurian as a hostage to get a prisoner exchange and needs her unharmed. Among those with him are a woman whose husband and son have been abducted, as well as the woman's father who has been poisoned by a Silurian attack. The Doctor is planning on going underground to negotiate with the Silurians. You'd Expect: The Doctor, having interacted with humans for so long and knowing that they are emotional, would keep the woman and her father with him so that they can't go Mama Bear or Papa Wolf on the Silurian, with the consequences that would entail. Instead: He leaves these two as part of the group guarding the Silurian, and the woman conducts a violent interrogation on her.
Also when Ambrose tasers Alaya... You'd Expect: Ambrose to simply leave Alaya alone after that, considering how remorseful she was. She also knew full well that Alaya was a Death Seeker who wanted her own death to spark a war between humans and Silurians. Instead: Ambrose, after being taunted by Alaya, electrocutes her to death which worsens Human/Silurian relations.
Missy no longer has a use for one of her subordinates - Dr. Chang - and very explicitly states that she's going to kill him after he says "something nice". You'd Expect: Him to run away. Instead: He obeys her, fully expecting her to listen to his pleas and not kill him, but she just vaporizes him in response.
Missy and Osgood are both in the same cargo bay and Missy claims that she has an "important secret" to tell Osgood but she has to whisper it. You'd Expect: Osgood not to listen to her and to stay at her computer. Instead: Osgood walks closer, allowing Missy to whisper in her ear that she's going to kill her! What's Worse: Is that even with this threat looming over her head, she doesn't run away, alert the guards or call for help. She just walks back to her computer and even when Missy starts a countdown and Osgood finds her handcuffs that are supposed to be restraining her in her pocket, she stays put and gawks at them, allowing Missy to sneak up behind her and vaporize her!