An unbroken flow from start to finish - the kind of thing where it's only paragraphed to stop eye-bleeding Doesn't matter if the thoughts themselves are jumping about, they will follow on from each other if it's done right, like stopping halfway through one thought and jumping to the next one that was triggered instead of waiting until the end of the first thought. Aside from that, just obviously has to reflect or be the inner thoughts of the character. You can write it 3rd person, as long as it follows the same rules.
the feelings and thoughts of the writer [or character, if fiction] written as they flow out non-stop, with no editing, no correcting of grammar, etc.
With the impression of no editing, correcting of grammar, etc. It can take a lot of editing to give the impression of stream-of-consciousness whilst remaining readable!
once you start editing/correcting, as when writing fiction, it's no longer actual 'stream of consciousness'... the real thing, not the fictional version, remains as it emerged, flaws and all... just as imperfectly worded/phrased/etc. as our thoughts are themselves... which is why, if writing s.o.c. inner dialog in fiction, one should not edit it to perfection, as you pointed out, dig...
