Unless you don't use social media at all, I don't think it's possible to avoid filtering the way you present yourself online. I don't post on Facebook much, nor tweet particularly often. When I do, it's mediocre in quality, but better than what I withhold. Even something as rudimentary as liking something on Facebook often presents me with an internal discourse because of how it may show up on the feeds of Facebook friends that I've liked a certain thing. When adding actual topics/subjects to my list of likes, I tend to do it at a late hour and in bulk, for example, 3AM, when most people will be asleep so if the "Piers likes [certain Facebook pages]' were to appear on other people's sidebars, I can remove it from public view. To be honest, it's quite a pathetic level of consideration.
The topic of my considerations when liking a Page is for another post though. Returning to the subject of filtering, photos are a key area affected by this. I went to Berlin over the holiday and took five hundred and sixty six photos. Only twenty one of which I uploaded to Facebook. On the Systems & Users field trips, I took four hundred and thirty two photos, but only uploaded fifty four. That's only 3.7% and 12.5% of photos that made the cut respectively.
This photo was dumped
This one was chosen
If I tweet something and then notice I made a typo, I will delete the tweet and post it again, but corrected. In a way, this is cheating, but it maintains an impression. After all, I doubt anybody reads my tweets, but I'd still rather the spelling was correct than not. With more publicly known people though, there's a difficulty. Whenever certain people tweet, within thirty seconds it could have been retweeted a hundred times (there are fans that are that concerningly attached). Even if they aren't that level of famous, it's still an awkward thing to do. For example:
In the first tweet, there's a typo, which he followed up with the second tweet a minute later. Interestingly, the first tweet had no replies and eighteen favorites. The second tweet, with less substance, got six replies and thirty favorites. Make of that what you will.
"Dance like nobody's watching" (attribution varies) is an interesting thought. Personally, I can't dance or sing in public because I think I'll come off as looking stupid. In private, I'm still incapable of singing, but I do dance. Exploring this quote further, I'd like to apply it to the masks we wear. Here's a spoiler alert for The Truman Show, so if you haven't yet seen it, skip the next paragraph.
In The Truman Show, the main character, Truman Burbank (played by Jim Carrey) thinks he is living an ordinary life, when in fact his life has been constructed around him since shortly after his birth for a reality show. In the end, he manages to escape into the real world.
This is slightly similar to Dark City and The Matrix in the realm of the 'world' being formed and controlled by others, always with a hero trying to escape. As far as we know, this world we live in is genuine. However, the internet is another world (but still a real world), where it is a lot easier to consistently create a different persona by. Online, it is a lot easier to be a gatekeeper than in the physical world, as you are mostly in control of what information about yourself you release. In the physical world, you let out all sorts of information from body language to mannerisms to spontaneous reactions.
Thinking about online perception, from 1996 to 2003 JenniCam existed where Jennifer Ringley broadcast her room online. Keeping up an act for seven straight years would be exhausting, so one can assume that although she knew she was on camera for the world to see because she set it up, she was her normal self. In Simpsons Comics #42, a Truman-esque scenario is portrayed, where Homer's life is broadcast without his knowledge, gaining a large audience that enjoy his stupidity and mistakes. Eventually he finds out, but instead of breaking free, he continues, and tries to be funny. In the way that you can't force humor, Homer's attempts to be funny were a disaster compared to the previous inadvertent entertainment value. While just a comic, it did explore how the behaviour of people can change when they know that they're being watched.