It doesn't seem different to, for example, 'hit' versus 'heat' in English.
It's definitely worth noting here that the english words "hit" and "heat" are felt by native speakers to use two different vowels (referred to as "vowel quality"), whereas the Latin "occido" and "occido" were felt to use the same vowel, in different lengths (referred to, oddly enough, as "vowel length"). That's why they're spelled the same.
Similarly, Japanese kana don't have different symbols for the short and long versions of their various vowels. Long vowels use the symbol for a short vowel, followed by a length mark.
English does use differing vowel lengths, but english vowel length is fully determined by other things; it doesn't vary freely. A standard example would be that the vowel in "made" is longer than the vowel in "mate".
I remember hearing an argument in a linguistics class that for English oral stop consonants ("p","b","t","d","k" and "g" at the end of a syllable), the primary source of differentiation between minimal pairs, like "made" and "mate", is vowel length and that they are all devoiced.
http://en.wikipedia.org/wiki/Vowel_length#Short_and_long_vow...
It's definitely plausible to me that (when the word is pronounced in isolation) word-final stop consonants are all devoiced. I haven't looked into the question at all and don't plan to, so I'm basically just spitballing. But my vocal tract can definitely start running down before I entirely finish speaking.
However, a much bigger issue than distinguishing "hid" from "hit" is distinguishing "hip" (where the final stop has become a glottal stop) from "hit" (ditto). I was under the impression that in general there isn't necessarily any phonetic difference at all there. If the argument you mention was only referring to minimal pairs with the same place of articulation, that sounds more reasonable.
When linguists say that a language has minimally contrastive vowel length, they mean that a single vowel can be pronounced with either a short or long duration, resulting in totally different words.
So in Khmer...
យឹត /jɨt/ means "to scold"
and
យឺត /jɨɨt/ means "slow"
A long vowel is indicated typically in the IPA either by doubling the vowel symbol as I did above or by placing a macron on the vowel (a line over the top, as in /ā/).
As was mentioned, the terms "long vowel" and "short vowel" learned in English class are misleading and bear no reality to the duration of English vowels.