Old Man Ho Oh: In "Death of the Doctor", Jo Jones' offhand line about the Doctor always getting into trouble with the Time Lords and the Eleventh Doctor brushing it off could be interpreted as the death of all of them before series 1 of Doctor Who... until you realize that he could be referring to that time he faced off with them almost a year before Death of the Doctor as they escaped the Time Lock in Doctor Who's "The End of Time".
EMY 3 K: In "Invasion of the Bane", Sarah Jane says that if she had a son, she'd name him "Luke". Luke means "beloved physician". In the Church, Luke is the patron saint of doctors and artists.
Sarah Jane's habit of walking up to the villains and telling them she knows their plans seems like a case of Too Dumb to Live. But the Fridge Brilliance kicks in when you realize: this is exactly what the Doctor does all the time, especially in his Third, Fourth, and Tenth incarnations, the ones that inspired her the most. Like Jack in Torchwood, Jamie, Bill, and Clara, amongst others, she's absorbed quite a few character traits of the Doctor from her time with him, and one of those is the habit of swaggering into enemy strongholds and announcing to the baddies that you're going to stop them (and then pulling off an Indy Ploy).
Other traits she's picked up from the Doctor: It's lampshaded in "The Eternity Trap" that a supposedly open-minded woman who's seen so much of the universe would be more willing to believe in ghosts. However, the Doctor hates labeling anything as magic, mystical, or unknown, and so too does Sarah Jane.
In "The Last Sontaran," she's originally a bit cold when Maria announced that she would be leaving, encouraging her to go. As she says, partially this is a defense mechanism, but it's also much the same thing the Doctor did with her when she announced that she was leaving him.
You'd think that Sarah Jane would've noticed the sounds of the TARDIS during "The Wedding of Sarah Jane Smith", since unlike the others, she's heard it before. But as we later discover, she's under subtle mind control, so she's not focused on anything not directly related to the wedding.
It makes a lot of sense that the Trickster never went after the Doctor. Aside from the fact that the Doctor is a much bigger threat than Sarah Jane, there's also the fact that without the Doctor, the whole universe would've been destroyed several times over. No universe, no chaos for him to enjoy.
That said, in "Turn Left", the Time Beetle that creates the horrifying parallel world around Donna where the Doctor dies in "The Runaway Bride " is said by the Doctor to have been part of "the Trickster's brigade." So while he never went after the Doctor directly, he got pretty close - if left to continue, the parallel world could have become permanent. Of course, it's unclear if the Beetle realized that would happen.
The nuns chanting "Serve the Gorgon" in Eye of the Gorgon is a bit hammy. However, it's all but explicitly stated later on that they're being mind-controlled by the Gorgon. Which then leads to the brilliance: They're not chanting it out of obsessive devotion, but rather because it's most likely the only thing they can think!
The lack of angsting over Andrea's fate at the end of "Whatever Happened To Sarah Jane" is actually justified by a combination of factors. First of all, with the meteor, everyone is no doubt focusing on the imminent threat. After that, Sarah Jane has had thirty years to mourn her friend, so while she undoubtedly respects and is grateful for Andrea's sacrifice, it's not new to her so much. In Maria's case, she's more concerned about Sarah Jane being restored to life than her neighbor dying, particularly given that, with Chrissy being...well, Chrissy, Sarah Jane is the stable, responsible, and empathic maternal figure Maria's always needed and never gotten, whereas Andrea was just her neighbor she had been friendly with for a matter of months. Alan is in shock and dealing with the revelations of what his daughter and her friends have actually been up to, and the fact that the universe is a million times more complicated than he'd ever realized. Meanwhile, Clyde only knew Andrea as the cool neighbor down the street, and Luke didn't exist in that timeline at all. So naturally neither of them would have any strong feelings.
Sarah Jane's arch-enemy picks up the name "The Trickster," despite it being what Alan called him. It actually makes sense when you realize that he exists outside of normal, linear time. So Alan called him that, he liked it and picked it up, then began identifying himself as "the Trickster," to the extent that the Doctor, Captain Jack, etc have heard of him under that name.
Martin Trueman calling on Clyde, Rani, and Sarah Jane during his show makes sense when you realize that the Ancient Lights give him some measure of foreknowledge. He's deliberately scouting out his potential enemies.
If Rani hadn't picked up the pendant in "The Mark of the Berserker," it almost certainly would've been picked up by either a teenager, janitor, or teacher, one very likely with little to no connection to the main leads. God only knows how much damage they might do before they were stopped.
From the same story, how many people might face disciplinary action from their jobs for letting clients just walk off with merchandise for free? Even though Paul says he'll return everything, it's doubtful he'll explain that he was using mind control.
Also, while Clyde throwing the pendant in the water is great, it's fairly likely it'll eventually wash up on dry land again...
Harsher in Hindsight: In "Secrets of the Stars", Martin Trueman reads Sarah Jane's past, accurately describing her time with the Doctor, how it ended, how she keeps secrets, and how she wins her battles. Then, he predicts that Sarah Jane will lose a battle in the future. This is one big continuity Call-Back for Elizabeth Sladen's character. Where does the horror come in? In real life, Liz lost her battle with cancer several years later.
One of the Slitheen in "Revenge of the Slitheen" is disguised as a child. Given that their disguises are the skins of dead humans...
The girl who helps Clyde in "The Curse of Clyde Langer" could have given a Line-of-Sight Alias as response to Clyde's own transparent use of the trope, but it is likely there was another reason that she isn't going by her real name, she is homeless in her mid teens. There are 2 main reasons for this that she could have, either she was kicked out of her home like Clyde was, or she ran away, most likely from an abusive parent. The mention of things "not working out" with her stepfather and the fact that she wasn't using her real name implies the latter, as well as some other horrifying implications...
The Trickster's attempt to go after Sarah Jane only failed the first time because of the Verron soothsayer's memory box, and later because she was savvy to his attempts. What happens if the Trickster goes after Captain Jack, or the Brig, or Vastra, or any one of Earth's other defenders? For that matter, how many times has he Ret Goned someone, and we don't even know?
We can assume he tried going after Donna in "Turn Left" through the Time Beetle, since the Doctor mentions it was part of the Trickster's brigade.