Mild sexual references (nothing children will get), flirting and kissing is seen.
In one episode, a character talked about going to a hotel with her boyfriend, but it was not followed up on.
Some explicit innuendos, again, nothing a child would get.
In the episode Blink, one character is seen naked from the top up and one character sees all of him. He then asks groggily if he was wearing pants and she declines.
At the end of Flesh and Stone, Amy acts suggestively towards the Doctor on the night before her wedding. She kisses him passionately and tries to undress him but he stops her, instead taking her to see her husband-to-be, Rory. However, there are no overt references to sex in this scene.
In the lodger, you see the top of the doctor while he is in the shower then you see him get out and drop his towel all you see is the top half you never see below his chest
In one episode, The Doctor has a conversation about how Rory and Amy's baby was conceived on the TARDIS making the child part time lord. He says "They don't put a sign up, it just happens!" referring to sex. Young children will not understand this.
In the Pond Life miniseries, the legs of a woman are shown standing in front of the Doctor, then a robe dropping.
In Season 6, there are various references to homosexuality, brief, and generally they do not have any effect on the plotline. They are simply there. In "Let's Kill Hitler," for example, there are two. In a flashback, Amy accuses Rory of being gay, and later, River Song approaches some Nazis saying "I was on my way to a gay gypsy bar mitzvah."
Some characters, for example Captain Jack Harkness, are openly homosexual, and kissing between members of the same sex is seen briefly in a couple of episodes.
In the 2013 Christmas Special, when Clara first enters the TARDIS Eleven is naked. She turns away, clearly uncomfortable. We see his legs and upper body; his midsection is always blocked by something. After a few lines of dialogue are exchanged, he presses a button, at which time a suit 'projects' itself onto him. However, when Clara takes him to meet her family, he reveals that only she can see the projection, meaning her family is seeing him naked, which causes them obvious discomfort. However, nothing is seen. Later, he takes Clara to a 'church' hovering over a planet and tells her to swallow a pill that will give her the appearance of being naked because "You can't go to church with your clothes on". However, she is still fully clothed to the viewers.