Small rationality-inducing cognitive algorithms that manifest in everyday speech:

1. " You're missing the forest for the trees." Given what you want to achieve, spending time on these details may not matter.
2. "For example?"
3. "What's the chance that that'll actually happen?" Think about the probability of the hypothetical. The notion that randomness and chance is something that can be measured is a rather recent phenomenon in human history.
4. "What's done is done." or "No use crying over spilt milk." Don't fall prey to the sunk-cost fallacy.
5. "I'm going to play the devil's advocate here." Steelmanning your argument.
6. "What difference does it make?" Does what we're arguing about actually have any consequences?
7. "You've got to take the long-term view." Don't think of the action you're considering as a single-shot thing, but more of as part of a strategy.
8. "They did this study..." What does the literature say? I agree that this move is often used to just support the argument you want supported; but hey, it's a step in the right direction.
9. "I don't get it." I notice that I'm confused.
10. "So let's be clear here." OR "Just to make sure that we're on the same page here." You and I may have different models, so let's ensure that we have the same model.
11. "This is win-win." Basically, a Pareto improvement.
12. "You do your job. I'll do mine." Benefits of specialization.

I agree that these phrases aren't very nuanced or advanced rationality techniques, but they're steps in the right direction. And to better is why we have things like Less Wrong.