I'm asking this question with fanfiction in mind, but I guess original fiction could work as well. For people who "publish" their work on websites (like fictionpress, or fanfiction.net, or maybe even forums as this one) I have a question: do you work your series out and post it only when it's finished, or do you post chapter by chapter? If you choose the latter: how do you deal with possible continuity problems? Maybe in the chapter you published today, character X has done Y thing in the past, and in the chapter you post tomorrow, he's done thing Z. It's sort of problematic for me because I don't really outline.
Surely that's just a question of logic? If you see yourself falling into the trap of constantly changing previous chapters because you are adding more and more things to the past, then you shouldn't post it until you are done. If you can put together a rough guide of where you are going with the story, then you shouldn't need to change major events in the past. Then, you know what the major things are and what you can't change at a later date. Everything else can be in relative flux and you can add or take away as you please. Alternatively, DO release it and allow the past chapters to lock you into a format. Potentially opening you up to work around situations you would previously have rewritten earlier chapters for.
If continuity is your problem, remember that you don't have to outline only before you write. Before you post an installment, write a synopsis or outline of that and review your synopses before you write thenext.
I would work it out first. It would be very frustrating for a reader to find blatant inconsistencies in a story. Also, your work is a reflection of you. You should want it to be the best it can be before you have a group examine it! This way you don't appear as though you don't take your writing seriously, and your critics aren't wasting their time pointing out mistakes that you already know about.
I don't outline either but I don't generally have a problem with that. Sometimes my characters will shock me, sometimes they'll remaine stable. For example, in a book I'm writing now, I wanted one character purley for comic relief. He decided that he was going to play a "rock", and be a great character, not just someone for comedy relief. Guess I was wrong. Fanfiction.net and other websites are fairly forgiving. However, when writing fanfiction, unless you decide upfront it's not cannon, individuals may get angry with you. Trust me, I know.