Never say no
One of the first things they teach you in improvisational acting is a rule that all roleplayers should know -- "No" is a bad word.
"So, instead of being perfect all the time, consider giving your character some disabilities or points of weakness."
"No" is a word that shuts down a scene before it starts. Roleplaying, especially pickup roleplays, thrive on creating possibility. When you use an action that completely stops another player in their tracks, when you disagree so strongly that it leaves the other player scrambling for any response, you're not only killing the fun for the other person. You're also killing it for yourself. For example, if someone in a scene says, "We should go look at the flowers in the Royal Garden," and you say no without any reason, how quickly does the scene die?
Now, this isn't to say that negative statements can always kill a scene. They only kill the scene when you leave no recourse for anyone else in it. So, instead of saying no, try to redirect. Using the example above, don't just say no. Say, "Well, the flowers don't quite interest me, but the statues outside of the castle do." Now you've disagreed but have provided another option, which keeps the scene alive and could spark some more dialogue. Why are the statues interesting but the flower garden isn't?
There is one time when a character can say no and walk away -- when the character would be forced to do something completely outside of his personality or against their beliefs. At that point, feel free to have the character walk out of a scene. But, remember, you can still apply a form of redirection to keep the scene interesting. Instead of just saying no, consider attacking the other person if it would enrage your character enough, or threaten to take them to the police, or some other option that keeps the scene alive and re-directs the conflict.Weakness is wonderful
Too frequently do roleplayers fall in the "god mode" trap. They'll create characters that are perfectly unstoppable heroes that are never wrong, are perfectly heroic, and will always save the day. That's boring.
Why is it boring? Story is based on conflict, and if you destroy all conflict before it even gets the chance to occur then you've pretty much just stopped the story dead in its tracks. So, instead of being perfect all the time, consider giving your character some disabilities or points of weakness.
Now these disabilities or weaknesses don't have to be physical disabilities nor do they have to be perfectly obvious. While a character blind in one eye is interesting, a character who's knee deep in loans is also just as interesting. Even a character's greatest strength can become their greatest weakness. I once played a paladin who was so fervently devoted to her faith that it drove her friends away. This character's greatest asset (her trust in her faith) was simultaneously an aspect of her character that offered a source of conflict (being completely obnoxious or unrealistic.)
These weaknesses can give others a way to relate to your character, to draw you into plots, and to experience some really interesting conversations. Some of my best roleplaying experiences come not from intense battles, but from sitting and talking with others in a bar over drinks.