An all-powerful evil conspiracy... could not oust rogue Agent Mulder and sympathetic Assistant Director Skinner from the FBI, or at least remove them to some insignificant bureaucratic duty? Explained (rather poorly) by the back story of Mulder having been regarded as a hero who aided in the capture of a vicious serial killer early in his career, and therefore any action against him would be a public relations pain in the backside. Not explained by the fact the Evil Conspiracy had already ousted people far more important and powerful.
Mulder was the Smoking Man's son, and he sacrificed his wife and Samantha to the aliens to protect Mulder. Krycek and the Well-Manicured Man were protecting him as well.
I always thought it was because no-one liked or believed Mulder; this way, anything he actually found out was guaranteed to be treated as a Cassandra Truth. In a way, Mulder was an extra layer of protection.
The conspirators may also have found him a convenient stalking horse, when investigating strange events that they weren't involved in. All those Monsters of the Week, for example.
Take it even further, actually: the Cigarette-Smoking Man always paid close attention to wherever and whatever Mulder went and did, and there are several hints throughout the series that, when it didn't interfere with their specific projects, the "cabal" had no problems implementing whatever safety procedure suggestions he would make regarding dangerous unexplained phenomena. To put it another way, Mulder was half a whistle-blower, half SCP agent. They would've been fools to have actually gotten rid of him completely, and they knew it.
It was likely a useless move. Mulder has shown that it doesn't matter if he is in the FBI or not — he'll go after the truth with or without their help.
He also had a few friends in high places himself at times.
"The Unnatural": The end scene has an aspect of Fridge Brilliance to it. Mulder uses the Hands-On Approach to teach Scully how to play baseball. The entire scene is based on Scully telling Mulder she'd never hit a baseball before, instead finding better things to do than "slap a piece of horsehide with a stick." This is most likely a lie. Scully was introduced as someone who defied female stereotypes and enjoyed being One of the Boys. Her mother tells Mulder in season two that she was a tomboy, unlike her sister. She got along well with her brothers, who gave her a BB gun for her birthday and showed her how to use it. Moreover, she was very close with her father and spent a great deal of time with him. The chances of her never hitting a baseball are pretty slim. But judging by the look on her face, she didn't mind being taught one bit.
"Arcadia:" Mulder and Scully go Undercover as Lovers to solve a case. Mulder mentions this is their first case since being back on the X-Files, but complains that it isn't an X-File at all. And he's right; though the case turned out to have paranormal elements to it, it was originally just a missing persons case in a seemingly perfect neighborhood. Which means that out of all the male/female partnerships in the FBI, whoever was in charge of the case thought that Mulder and Scully would be the most believable as a married couple.
The title of "Red Museum". Largely meaningless in the context of the episode - but on a meta-level, it's a collection red herrings. Enough to fill a museum perhaps...
It's not meaningless; the "control group" in the episode is a religious group who call themselves the Church of the Red Museum. Mulder even asks the significance of the name. The leader took his congregation to cattle country and bought a ranch, turning "500 head of cattle into pets." The leader called it a "monument to barbarism" as the whole population was vegetarian. The vegetarianism is relevant to the plot, since not only were the children in this church not getting the inoculations of growth hormone the other kids were getting, they also weren't eating the beef and milk from the cattle who were also getting the hormones.
In "Clyde Bruckman's Final Repose", the titular character tells Scully she won't die. One wonders how that's possible, till we reach "Tithonus", where an immortal photographer apparently gives up his immortality in order to save Scully, taking her place. As this is how he stated he became immortal in the first place...
The doctor also notes that Scully is recovering from her gun shot wound at a faster rate than the doctor had ever seen...
Quite a bit, but the most notorious example might be from Fight the Future: how did Mulder and Scully get back to civilization from the crashed spaceship in the Antarctic? (There's a joke about this later in the TV series.)
Okay, "Home" is a great and chilling episode, but does anyone else think the writers didn't put much thought into that ending? The surviving Peacock family hit the road with plans to start over their grotesque family elsewhere, but how in blazes do they hope to pull that off? The only way they had managed to hide from society for so long was because of their ancestral farmhouse, which they no longer have by the end, and in the course of the episode they had murdered two law-enforcement officers and one's innocent wife, so there's no doubt whatsoever that police will be actively looking for them. Since they aren't supernatural villains with any reality-bending powers, it's a pretty safe bet that the minute their car runs low on gas or they need to find food, Peacock Jr. and his incestuous potato-sack of a momma are fucked.
Easy Logistics played for the Rule of Cool: Mulder never ever has any qualms about commandeering any resource from the FBI, regardless the cost, which strikes as unrealistic when everyone knows he is acting on suspicions, insignificant clues and in most cases outside the rule of law, full stop. Airplane (possibly military) transport, all-terrain tracked vehicle, supplies by ton for the Antarctic trip. No higher FBI official batted an eyelash on such extravagances ever.
The girl handling the agents' finances was later revealed to be a huge fan of the agents, so she probably didn't treat any of Mulder's actions as unnecessary.
Mulder is also implied to have come from a wealthy family; he grew up on Martha's Vineyard, his parents owned a summer house in Connecticut, he went to Oxford for college, and he "rents" a Congressman for his own uses. In season 8, he's unconcerned about his own unemployment and doesn't try to get another job. After that, he's able to easily slip into hiding and support himself while doing so. It could be that he's not using FBI channels or money at all, but his own money to fund some of his more ambitious expeditions and his friends in high places (see the rented Congressman) to grease the wheels.
"Darkness Falls" episode (1994) does it at least twice. The Monsters of the Week, basically vicious blood-sucking bugs, are "afraid" of light in Mulder's words, in practice they are inactivated by light. Our heroes and a few others are caught at night in stranded cars, but with fully operational engines and electrical systems. Why didn't they turn on the headlights and interior dome lights? And how could the bugs after killing a 70-90 kg (155-200 lbs) man raise his body onto a tree? (Although the last one can be explained by the fact the victim could have been killed while he was already up in the tree, since he was a logger).
There was supposed to be critically short fuel supplies, making escape (or even cabin lighting) via the vehicles impossible. What struck me as odd is why they didn't maintain a small to medium reserve to use as an extreme form of lighter-fluid, and use it to start campfires that, once going, would have the unlimited fuel of the forest.
Speaking as someone who's grown up in The Other Rainforest, at that location and time of year, any wood they didn't have chopped and stacked under cover was probably too damp to burn. Even lighter fluid sometimes isn't enough to keep a fire going, if it's too soggy.
Scully giving William up for adoption in season 9 is a source of Fridge Logic for a lot of fans. In the first place, it goes directly against Scully's character, who only four seasons before had fought tooth-and-nail to adopt a three-year-old daughter she'd never met and had only known three days. All this despite knowing that the child was conceived to be experimented on and that both mother and daughter would likely be hunted by the conspiracy. In the second place, it doesn't make sense from a common sense standpoint. Scully gives William away to an anonymous couple in order to keep him safe. Never mind that she is taking the baby away from at least five trained FBI agents who know the details of the situation and have the weapons, knowledge, and training to at least try to keep him safe and giving him to a couple who know nothing about the baby's paranormal background, the conspiracy, or the fact that they now have a huge bulls-eye painted on their backs. To make it worse, this is a closed adoption—there is nothing Scully can do to check on her baby after she gives him up. Doesn't this just make it easier for the conspiracy to kill of William and his adoptive parents?
The season five episode "Folie à Deux" has a nice little whammy. A guy in an office building can see a bug monster disguised as his boss (which no one else can see) turning his co-workers into zombies (which no one else can see either). He sends a tape to a radio station containing a warning telling everyone to band together and hunt down the monster that 'hides in the light.' Eventually, he gets desperate enough that he pulls out an assault rifle and takes everyone hostage, separating out the 'zombies' from the real people and even getting his bug boss singled out on the floor right in front of him. He then... threatens to start shooting real people unless he gets on TV. He has both the bug and the zombies RIGHT THERE, why doesn't he just shoot them now?
In "The Calusari", we know Michael, who is essentially a ghost can travel around and physically harm people. He's a lot creepier and more emotionless than Charlie... which is exactly how the boy in the opening appears. Which means that kid might have been Michael, not Charlie, which then makes one wonder, how often has that happened? How many times have the parents walked around thinking they were with Charlie, and instead had the dead one?
In the first part of the Season Eight finale, Doggett calls his friend Agent Crane in on the weekend to help investigate a murder, which Crane mentions caused him to miss his "kid's Little League game." Then at the end of the episode we find out that Crane is one of the alien Replicants with the bumpy metallic spines. Assuming that he does have a family, they're living with a murderous alien and are absolutely none the wiser...
Or, even worse, he was replaced before he met his wife and had a family. That means his child is a Half-Human Hybrid and just hasn't realised it yet.
"The Jersey Devil"'s ending; both of that... child's (I refuse to use the word "creature") parents are dead. That means she's either going to starve to death or a pack of passing coyotes will decide "ooh, easy lunch" and eat the poor child alive. Poor kid.
And, to say that the female Jersey Devil deserved to die (like some critics who reviewed the episode) is just cruel. She was trying to escape, and was not actively attacking Mulder, Scully or anyone else. Despite her, ahem, dietary preferences, Mulder's shock at the fact the resident Corrupt Cop killed her is entirely justified. And makes us hate the Corrupt Cop more.