To be fair, Continuum hasn't yet spelled out the "rules" of time travel. But thus far, the show appears to be in the grand tradition of Star Trek, Doctor Who and other series that made up the rules on a case-by-case basis, as they went along. We're already seeing plenty of apparent contradictions in the way time travel seems to "work."
The most tongue-in-cheek part of the above clip is where Emily references the Novikov Self-Consistency Principle, which basically claims that it's impossible to create any time paradoxes — and thus, for all intents and purposes, you can't change the past in any meaningful way. Alex sort of shrugs and says that most of the time, you can't create paradoxes, but sometimes you can.
What's especially funny about that is, the rest of this episode is basically proving that, in the Continuum universe, you can change the past. You can change it plenty.
The main plot of this episode has to do with a serial killer, known as the Ouroboros killer, who remains a famous unsolved case in the future Kiera comes from. This killer is active once again in Vancouver — the murder capital of Canada according to Continuum — and Kiera is determined to crack the case. Novikov would say that Kiera is doomed to fail, because she remembers this case being unsolved.
But instead, Kiera actually does crack the case, saving 30 pedophiles from being brutally murdered, with the eyelid removal and the doll gag and stuff. She pretty much proves, if any doubt remained, that time travelers can change the past. What's more, it seems as though she still remembers the case having been unsolved in 2077, after she solves it. (Perhaps there's a latency period, or perhaps she will always remember the timeline she comes from. I'd prefer the latter, but who knows.)
And meanwhile, in one of the episode's subplots, Kellog attempts to invest in a guy who will revolutionize the world with his new microbial reverse electrolysis method, which generates electricity and clean water simultaneously. You get the sense that in the "original" timeline, this inventor toiled in obscurity for years before finally making it big, but Kellog wants to hose him with cash now. Except that Escher, the time-traveling bigwig behind Piron Corp., beats him to it.
So assuming you can change the past, then we're a lot closer to the storyline promised in the show's opening credits, one in which terrorists and crooks from 2077 are trying to "corrupt or control the present in order to control the future." Which is a premise that only works if you can change history, after all.
This episode could have been a really boring filler episode — a stock "catching a serial killer" story with a bit of time-travel jiggery-pokery stuck on to it. Instead, it's actually pretty great — the serial killer stuff is fast-moving, and more entertaining than last year's episode about the murder of the scientist who was developing clean energy. But also, this turns out to be a very significant turning point for a number of the show's storylines, in a way that proves Continuum isn't afraid to keep moving the ball forward.
First of all, it's now more or less official — Kiera has given up on trying to preserve the timeline she comes from, at all costs. She's still desperate to keep her future more or less intact, but she's not willing to be entirely ruthless about it. She doesn't even hesitate, this time around, to stop the serial killer(s) and save those 30 pedophiles from a grisly fate — even though, as she tells Carlos at the end, she's making major changes to the timeline just by herself, even apart from what the other travelers are doing.
Second of all, of course, the "Kiera is lying to her fellow cops" storyline moves forward in a number of ways. Most notably, Carlos finally stops being a patsy and swallowing Kiera's "intuitions" about stuff — and she's forced to tell him the truth, which he eventually decides to believe after falling on Occam's Razor. (And with this episode, Carlos regains a modicum of respectability once again, and becomes a character you're not embarrassed to root for.)
But also, nobody in the Vancouver PD is really trusting Kiera any more, and her new boss quite correctly observes that all of Kiera's solves turn out to be lucky breaks.
Then there's the fact that Kiera finally meets Escher — who we were previously told was impossible to find, but apparently just hangs out in the Piron offices, taking meetings with Kiera's ex-boss Dillon and making cryptic utterances. The scene between Kiera and Escher is the most frustrating part of the episode, since it's in the grand tradition of "conversations where nobody will answer a simple question." This scene reminded me of some of the Olivia-William Bell scenes early in Fringe season two, where Olivia has crossed universes to get some answers and Belly just serves up riddles, because the show's writers don't want to give away the whole game too early.
In any case, it seems moderately clear that Escher is working against Kellog, and maybe against the Liber8 crew in general. He either sympathizes with Kiera's stated aim of preserving the timeline, or sees her as a useful pawn, or both.
And then meanwhile, Alec's dating the perfect girl (Magda Apanowicz, reprising her "nerd love interest" role from Kyle XY) who not only likes to geek out about time travel but also puts up with his painful moments of dorkiness like announcing "I'm uploading this to my hard drive." She kind of manipulates him into taking her to the super secret lab that Kellog set up for him, which leads to Kellog going apeshit — and Kellog turns out to be right, because she's apparently working for someone.
So we're roughly at the halfway point of season two, and it's already clear that this is a way better show than it was in season one. There hasn't been a single episode as weak as some of the middle episodes of the first season, when the show seemed to be spinning its wheels somewhat. Pretty much every episode of season two, thus far, has been either good or great, which is highly encouraging. Even if this show ends up being every bit as sloppy about its time travel as Looper, it's showing every sign of telling a fantastic story along the way.