For a series that was originally conceived as an Edutainment series for kids, Doctor Who, especially in the new series, has snuck a few past the TV code (for the most part, these are from the 2005-present revival series; the original 1963-89 series tended to attract more concern about violence than innuendo).
The Doctor Dances: the Doctor discusses "dancing" with Rose, a little miffed that she assumed he'd never "danced" before. He has, it's just been a while. Later, when the Doctor and Rose are dancing note the literal kind of dancing in front of Jack, Rose assumes that Jack wants to cut in and dance with her. As it turns out, he'd rather "dance" with the Doctor.
Dalek: Viewers were apparently so upset over a reference (in a sexual context) to "spooning" (lodging a number of complaints) they appeared to miss the fact one of the characters in this episode utters the strong (even for 2005) swear word "goddamn," which as of 2013 remains the strongest word uttered in the main Doctor Who series (for stronger language, you need to watch Torchwood).
That may be dependent on your location - in the UK and in Australia, neither "damn" nor "goddamn" are really considered swearwords.
Cassandra: She's back! Oh, that little blonde bi- (Cut to the Doctor and Rose talking) Rose: Bit rich, coming from you. And later: Cassandra: That portion of skin came from the front of my body. This... came from the back. Rose: Right, so you're literally talking out of your ar- Cassandra: Ask not. And in the (in)famous body-switching scene: Cassandra/Doctor: I'm a man! So many parts... and hardly used. (humid look at Rose)
And some of it's not even that subtle. In a family show, a line like this was bound to have children blinking in confusion.
At some point in "The Impossible Planet"/"The Satan Pit" two-parter, several characters are crawling through a duct.
Rose: (right behind Danny) Not your best angle, Danny. Danny: Oi, stop it. Toby: (behind Rose) Mine could be worse. Rose: Oi!
In "The Christmas Invasion", Rose remarks that the Doctor has two hearts.
Jackie: Anything else he's got two of?
For an added bonus, Jackie is clearly looking at The Doctor's crotch while she says that line.
In "Love and Monsters", Ursula gets reduced to a face in a pavingstone. Elton remarks that they "still have a bit of a love life".
Then there's this from the 2007 episode The Lazarus Experiment.
In the mini-special "Time Crash," The Tenth Doctor mentions to the Fifth Doctor (their TARDISes intersected when Ten was redecorating) that the Master was running about again. Five asks whether or not the Master "still had that rubbish beard." Ten responds that no, but he does have a wife.
"The Eleventh Hour" has The Doctor run into a man he met earlier to use his laptop. When he snatches the computer away and looks at it he says "Blimey! Get a girlfriend!" — and later on: "Delete your internet history". Bravo Moff.
Okay, who here actually believes that Amy shows up to parties in skimpy outfits to kiss people?
Hey, a kissogram is actually a thing, costumes and all. They're just a bit... quaint. And hence fitting for Leadsworth.
And in "Flesh and Stone" there was the scene in Amy's bedroom, how the hell did they get away with that?!
They almost didn't.
There was a hilarious example in "Vampires of Venice," in which Rory pulls out a tiny light to ward off the vampires with. In response, the Doctor immediately pulls out a massive ultraviolet bar. Cue:
Rory: Yours is bigger than mine. Doctor: Let's not go there.
To make this even more remarkable, that's her daughter she's talking about. Although she and the audience don't know that yet.
And in "Vincent and the Doctor" the monster seems to rather enjoy one of the sonic settings.
The monster even returns the favor by repeatedly bumping a door that Eleven is leaning against. Eleven has a visible reaction.
In A Christmas Carol Amy and Rory are wearing their policewoman and Roman costume throughout the whole episode (having just had their honeymoon interrupted), and always change the subject when someone brings their clothes up.
Rory: You know, history lesson, a bit of fun every now and then, a bit of nostalgia!
Some not so subtle exchanges from the 2011 Comic Relief special:
Amy: He's just jealous because I passed my test first time. Rory: You cheated, you wore a skirt. ... Did you ever see Amy drive, Doctor? Doctor: No. Rory:Neither did her driving instructor.
Rory then, while working under the glass floor of the TARDIS, manages to mess up the systems pretty badly from not concentrating. Amy explains why it was her fault:
Rory: Heh..no. Why do I get slapped? Doctor: Because we have to stick to the established chain of events. One mistake and the whole timeline could collapse. We'd end up with two Amy Ponds forever, and then what would you do? Rory:[looks at Amy with raised eyebrows] Amy: *gasp* *slap*
In "The Impossible Astronaut":
Doctor: Shout if you get in trouble. River: Don't worry, I'm quite the screamer. Now there's a spoiler for you...
In Curse Of the Black Spot, the Doctor thinks the pirates are compensating for something with their guns.
The not-so-subtle exchange between Madame Vastra and Jenny in "A Good Man Goes To War":
Vastra: Was I being insensitive again, dear? Jenny: [gives her a look] Vastra: I don't know why you put up with me. [shoots out long, prehensile tongue]
Later, in The Snowmen, Vastra is shown in close-up outright leering at Clara. Surprisingly, Jenny doesn't comment.
The Wedding of River Song: "River Song came twice."
The "Night and the Doctor" minisodes have some...interesting lines. Examples from "First Night":
Doctor [regarding his and River's destination]: You could read a book by [the stars].
River [suggestively]: Is it okay if I don't?
Doctor: We've got ten minutes to get dressed.
River: Oh, that's so close to the perfect sentence.
a bit later
Doctor [referring to the diary]: From now on, there are rules.
River: Ooh, Doctor, you've got all strict—not that I mind.
From "Last Night":
[The Doctor is trying to resuscitate a Future!River, who's playing dead, and then—]
Doctor: River...you are holding your breath.
Future!River: You're a fine one to talk about holding. How many hands do you have?
Doctor: River, you can't do things like that!
Future!River: Or what?[...] What else are you gonna do, spank me?
[yet another Future!River enters the TARDIS, followed by her Future!Doctor]
Future!River II [sees Present!Doctor]: Two of you! The mindraces, does it not?
[Future!River and Future!Doctor leave, just as Present!River returns]
Present!River [seeing Future!Doctor]: Two of you! The mindraces, does it not?
With none of this taking into account a certain dress.
In the 2011 Christmas Special "The Doctor, The Widow, and the Wardrobe," there is a scene where, in order to save a planet full of sentient alien trees, the titular widow, Madge, takes the collective "souls" of the trees inside herself. During this process, she seems to be having an orgasm.
Doctor Who is classified as a children's/family show. "The Time Monster" has the Master on Earth making a teleporter that pushes matter through time and space called "Transmission of Matter Through Insterstitial Time". They even use the abbreviation TOMTIT. One investor gets mad at the expense and that the machine doesn't seem to work properly. "Even the name is offensive! tomTIT", with an emphasis on the last three letters. And STILL nobody in the censor board noticed.
In Britain, "tit" also refers to chickadees (which are actually a mostly old world family anyway). And that's the definition that the word tomtit is based off.
The Series 6 trailer had a naked River, though anything cleavage-based wasn't seen. Spoilers, indeed... They lied to us. It never shows up.
"Handcuffs! Why do you always have handcuffs?"
Followed by "You. Me. Handcuffs. Must it always end this way?"
In Smith and Jones there's a poster on the wall, just for a second, if you look closely, that says "condom facts".
Which is reasonable - they are in a hospital.
Amy's Choice had this fun little exchange:
The Doctor: I don't know, but I can't feel my feet... And other parts. Rory: I think all my parts are basically fine. The Doctor: Stop competing.
Asylum of the Daleks has, at the end of the episode, Amy and Rory - their relationship repaired - standing outside their house. Amy gives Rory a steamy look and walks inside. He smiles for a second, fist pumps, and follows her.
"Pond Life" part two has one combined with a noodle incident- The Doctor bursts into Amy and Rory's bedroom, only to immediately cover his eyes and yell at them to "stop what [they're] doing!" They were only sleeping, but considering they also have a rule about the Doctor bursting into the bedroom…
Amy was probably wearing either a bra of lingerie under the sheets, as she's clearly hiding her breasts while Rory allows his plain, blue T-shirt to be seen.
Also, at the end, Rory says, "I really hate it when he does that," suggesting that the Doctor has walked in on them more than once.
Surprisingly, the Hartnell era of all times could give the New Series a run for its money in the sex department.
In "An Unearthly Child", Ian suspects Susan might be sneaking into the Junkyard to 'see a boy' (innocent enough out of context, but bear in mind she's sneaking into an abandoned Junkyard in the middle of the night, suggesting that Ian thinks she's got more than holding hands in mind).
A jailer in "The Reign of Terror" pretty much offers to let Barbara go in return for sex. Thankfully she doesn't oblige.
Vasor tries to rape Barbara in "The Keys of Marinus".
Barbara was almost raped again in "The Romans", this time by Emperor Nero.
Edith is raped off screen in "The Time Meddler", confirmed by Verity Lambert on the DVD commentary. She also explains why the Hartnell era had a higher concentration of sex references; while social taboos were stricter due to the recent introduction of TV, there was less in the way of strict rules on content. There was more of a general consensus on what was appropriate for broadcast, and whether you breached it came down mostly to the whim of the producer.
This little gem from "The Myth Makers": 'Upon my soul, you're making me as nervous as a Baccante at her first orgy.' Steven Moffat at least tries to disguise his dirty jokes.
A soldier can be seen reading a porno magazine in "Invasion of the Dinosaurs".
Dinosaurs On A Spaceship has two distinct moments:
Brian Williams has balls in his pants. Golf balls.
"You need a man of action and excitement - one with a very large weapon!"
This one is even lampshaded by Amy, who calls him a "walking innuendo".
From "The Angels Take Manhattan," Melody Malone and her "cleavage that could fell an ox at twenty feet." The Doctor's clearly enjoying himself reading too, given the "Yowza!"
It's really not so bad considering it's River Song and therefore his wife.
On the other hand, he's reading it in front of her mother, and River herself wrote it.
According to the behind-the-scenes publication The Doctor Who Companion: The Eleventh Doctor Vol. 6, the original script would have had the Doctor utter the phrase "Traffic was a bitch." Evidently either Steven Moffat or the powers that be thought better of this and changed the dialogue.
In "The Bells of Saint John", the Doctor orders Clara to get into the police box, now (for their safety). A Motor Mouthed conversation where Clara obviously thinks the Doctor was propositioning her ensues.
The Doctor enjoys his Jammy Dodger a little too much.
River has a subtle Showing Off the New Body moment in "Let's Kill Hitler" when she walks offscreen for a few seconds to (it's heavily implied) check out her new body's butt in a mirror. We only hear her shrieking in delight, and later promising that she's "going to wear lots of jodhpurs!" Because it happens offscreen, it's not blatant enough to count as outright Fanservice. And the joke is only obvious if you know what jodhpurs are.
Even moreso, when you consider that she's wearing a loose-fitting dress in that scene—meaning that she'd have to have deliberately lifted up her dress to get a good look at her bottom. Which would be way too saucy to show on-screen on an episode of Doctor Who.
The Second Doctor serial "The Wheel In Space" gives us the classic Patrick Troughton line fluff "We're all going to be killed shortly unless you switch over to sexual air supply."