I think whether reality checks make you more rational largely depends on what sorts of checks you are using. There are many checks that exploit "surface-level" features of dreams-- most commonly inconsistencies in clock faces and written text upon second looks-- in order to determine whether one is dreaming. These checks are useful for determining whether you're asleep but generally limited otherwise.
However, there is one somewhat deeper feature of dreams that IMO provides a more useful opportunity both for reality checks and for rationality practice. Dreams, by their very nature, lack a logical underpinning for events. We tend to find ourselves in the middle of a series of events without much explanation for how or why we arrived there.
Thus, one reality check that I find useful both in dreams and waking life is the thought "where am I, and how did I get here?" For instance, right now I am at my computer, typing a LessWrong post. I got here from waking up in my room and walking downstairs. I got to my room from driving my car after a party with friends last night.
Obviously, this type of reasoning can go on and on. The interesting part is that dreams lack this.
For instance, I recently dreamed that I was on an airplane. I thought to myself "How did I get on this airplane?" Realizing I had no memory of getting to the airport, I became lucid. You might wonder how this applies to rationality. The answer is that "Where am I and how did I get here" can easily apply not only to physical reality, but also to your mind and thoughts. Indeed, it is very similar to "What do you think you know, and how do you think you know it--" one of the classic questions of human rationality.
In my experience, internalizing the general form of this principle has been very useful both for dream checking and for improving rationality.
Great answer, I know this is something I need to do more in life anyway. So I did a little bit of it just now. Sudden increase in levels of curiosity[so virtuous. Wow.]. I'm so curious I even want to know crap like why my housemate sometimes leaves a spoon stuck in the coffee grounds of the compost container. Obviously they used the spoon to move the grounds in there, but why did they leave it stuck there rather than moving it to the cutlery dip in the wash basin? Now that is an extraordinarily minor detail- take that as an indication of just how motivating it is to suspect that you don't look closely enough at the details of your life to know whether you're in a shoddy simulation.
Note: this post is no longer endorsed by the author, for reasons partially described here.
In the spirit of radioing back to describe a path:
The truly absurd thing about dreams lies not with their content, but with the fact that we believe them. Perfectly outrageous and impossible things can occur in dreams without the slightest hesitance to accept them on the part of the dreamer. I have often dreamed myself into bizarre situations that come complete with constructed memories explaining how they secretly make sense!
However, sometimes we break free from these illusions and become aware of the fact that we are dreaming. This is known as lucid dreaming and can be an extremely pleasant experience. Unfortunately, relatively few people experience lucid dreams "naturally;" fortunately, lucid dreaming is also a skill, and like any other skill it can be trained.
While this is all very interesting, you may be wondering what it has to do with rationality. Simply put, I have found lucid dreaming perhaps the best training currently available when it comes to increasing general rationality skills. It is one thing to notice when you are confused by ordinary misunderstandings or tricks; it is another to notice while your own brain is actively constructing memories and environments to fool you!
I've been involved in lucid dreaming for about eight years now and teaching lucid dreaming for two, so I'm pretty familiar with it on a non-surface level. I've also been explicitly looking into the prospect of using lucid dreaming for rationality training purposes since 2010, and I'm fairly confident that it will prove useful for at least some people here.
If you can get yourself to the point where you can consistently induce lucid dreaming by noticing the inconsistencies and absurdities of your dream state,[1] I predict that you will become a much stronger rationalist in the process. If my prediction is correct, lucid dreaming allows you to hone rationality skills while also having fun, and best of all permits you to do this in your sleep!
If this sounds appealing to you, perhaps the most concise and efficient resource for learning lucid dreaming is the book Lucid Dreaming, by Dr. Stephen LaBerge. However, this is a book and costs money. If you're not into that, a somewhat less efficient but much more comprehensive view of lucid dreaming can be found on the website dreamviews.com. I further recommend that anyone interested in this check out the Facebook group Rational Dreamers. Recently founded by LW user BrienneStrohl, this group provides an opportunity to discuss lucid dreaming and related matters in an environment free from some of the mysticism and confusion that otherwise surrounds this issue.
All in all, it seems that lucid dreaming may offer a method of training your rationality in a way that is fun,[2] interesting, and takes essentially none of your waking hours. Thus, if you are interested in increasing your general rationality, I strongly recommend investigating lucid dreaming. To be frank, my main concern about lucid dreaming as a rationality practice is simply that it seems too good to be true.
[1] Note that this is only one of many ways of inducing lucid dreaming. However, most other techniques that I have tried are not necessarily useful forms of rationality practice, effective as they might be.
[2] And, to be honest, "fun" is an understatement.