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Factual error: Alba Bewick tells Oliver that she wanted to have twenty-six children. Her first child, Alpha, did not survive; her second was her daughter Beta. Oliver tells her there aren't twenty-six letters in the Greek alphabet, there are only twenty-three. There are in fact twenty-four. [This is quite possibly the character's mistake rather than the author/director's. There is a scene later in which Oliver and Oswald playfully and deliberately give Beta bits of obviously wrong information (00:39:27). Besides, director Peter Greenaway delights in playing games with his audience - to put it mildly. Also, at one point Oswald mentions that Vermeer painted twenty-six paintings, of which three are dubious (00:35:13-15). This gives us the same totals as Oliver's two alphabets. Was a connection intended (whatever the point might be)? At another point (00:53:12), Oswald catches Oliver in an egregious error, establishing his fallibility.]
Factual error: Oswald says that "Vermeer only painted twenty-six paintings and three of those are dubious." There are in fact thirty-five known to be extant (one recently stolen) of which only one is regarded as dubious. In addition, there have been descriptions of six (or possibly eight) others that seem to be missing.
Deliberate "mistake": When Venus de Milo walks toward the back of the fluorescent "ZOO" sign (presumably on the way to her death at the hoofs of the zebras), the "Z" is reversed (that is, it appears unreversed on the back of the sign). This gives the first three letters of the word "ooze," doubtless because that is what Venus will return to. (The word "ooze" is used earlier in the film in just such a context (00:34:35-00:35:50).) A tree blocks the space where the "e" would be (or rather would not).
Plot hole: At the end of the movie, snails collect on the apparatus on which Oliver and Oswald have set up a time-lapse camera to photograph their decaying bodies, eventually short-circuiting the camera and wrecking their experiment. As they had previously (01:34:18) set up similar apparatuses in the same area (Alba's country estate) photographing other decaying organisms, why didn't the snails collect on them? (Pleasant film, huh?)