Growing the Beard: Considered to be this for the revived series in general. Christopher Eccleston was a great Doctor, but in the previous episodes, most of the the monsters were of the quirky and wacky sort, save for maybe the Autons. Here, he faces the most iconic monster of the show, and takes the Darker and Edgier aspects of his personality Up to Eleven. This is the episode that cemented the reputation of the revival series, and it hasn't looked back since. Some people even said that it wouldn't be Doctor Who without the Daleks, and that this episode made the Daleks "scary" again.
Harsher in Hindsight: As seen in the picture on the Recap page, Rose is still wearing Mickey's sweetheart ring. Come "Boom Town", that relationship will be a thing of the past.
Similarly, there is mention of a meteor landing in Russia in 2013. Fast forward to 2013 and...
There's also his remark about owning the internet. Fast forward to 2012 and SOPA, and it nearly became a reality.
Some Anvils Need to Be Dropped: Though the choice of the Doctor and a Dalek for this moral is questionable, the idea that turning to merciless violence as a means of combating a hateful person will bring you down to their level is one that is delivered exceptionally well.
Strawman Has a Point: The Doctor wanting to kill the Dalek and wipe out their species is portrayed as bad, except he knows how dangerous the Daleks are, which is aptly demonstrated in this episode when the Dalek kills hundreds of people, and the Dalek makes it quite clear it wants to wipe out humanity. Rose tries to give the moral judgement, except she doesn't know about the Daleks, so this is out of ignorance. Later, she is terrified of the Daleks and shows no remorse on wiping them out (apparently). The Doctor actively torturing the Dalek was going a bit far, but him being ready to kill it certainly seems justified.
While "Remembrance of the Daleks" was the first successful attempt at showing a flying Dalek on-screen, it was clearly limited by the production team's ability to move the physical Dalek props. This time around, that's no longer an issue thanks to CGI, and the lone Dalek demonstrates to spectacular effect what it can do with flight.
On a similar note, the new extermination effect. "Remembrance" only had the budget to show one such extermination, and with graphics that may have been impressive for the time, but are somewhat cartoonish in retrospect. Advances in technology allowed this episode to once again perfect what "Remembrance" had pioneered.
The new Dalek design itself is an example, and quickly became near-universally regarded as the definitive Dalek design by fandom and casual viewers alike. It's likely that there would have been a massive backlash over the attempt to replace it in "Victory of the Daleks" even if the New Dalek Paradigm hadn't been regarded as such a bad redesign in its own right.
The Woobie: A Dalek as a Woobie? It's the first Dalek seen in the revival series. Tortured into near-insanity; alone in the universe of space and time; cut off from orders and companionship; forced to pollute itself to regain power; adapts to survive, in the process becoming "no longer pure Dalek". Cannot kill its enemies; admits fear and disgust at itself. Then is finally Driven to Suicide. "This is not life. This is sickness." A different set of values, but definitely a Woobie.