Not sure if a detailed list is possible; there's just too many of them, heh. It became evident even long ago, without the scientific analysis processes and tools.
Even pre-enlightenment era:
"If the Deluge had carried the shells for distances of three and four hundred miles from the sea it would have carried them mixed with various other natural objects all heaped up together; but even at such distances from the sea we see the oysters all together and also the shellfish and the cuttlefish and all the other shells which congregate together, found all together dead; and the solitary shells are found apart from one another as we see them every day on the sea-shores.
And we find oysters together in very large families, among which some may be seen with their shells still joined together, indicating that they were left there by the sea and that they were still living when the strait of Gibraltar was cut through. In the mountains of Parma and Piacenza multitudes of shells and corals with holes may be seen still sticking to the rocks...."
The most obvious reason is arrangement. If it was one big event in which everything died, it would be more or less one big mess of things with no particular arrangement; rabbits, velociraptors, and trilobites corpses all clumped together. But instead, we see the very distinct evolutionary history which appears very different, with the clear progression of organisms going deeper in the rock.
There's radiometric dating which, again, is altered by the YEC alternate science (or more specifically, they believe nuclear decay rates have dramatically decreased over time). Radiometric dating backs up the arrangements of progression previously seen, as well as showing a vast difference in time scales.
The formation of the quantity of fossil fuels we have also takes much longer than the asserted time. This particular one is either countered with more bad YEC alternate science or explained as 'God put it there as a natural resource for us.' The 'God dunnit' excuse is much more common here than the fossils example, as fossil fuels do have a practical use, whereas with fossils you're stuck precariously close to being between your pure deity trying to trick you or your devil who only has the power to corrupt actually creating things.
I'm sure there are dozens, if not hundreds, of others, but those are some of the most obvious examples.
As for the alternate YEC version of science, that originates from this:
http://en.wikipedia.org/wiki/Wedge_strategy (summary)
http://evolutionwiki.org/wiki/Wedge_document (original document)
It's pretty insidious. Their goals, from the horse's mouth are:
"To defeat scientific materialism and its destructive moral, cultural, and political legacies"
"To replace materialistic explanations with the theistic understanding that nature and human beings are created by God"
Or in summary, they are setting out with aims no less than the utter destruction of science followed by replacing it with far-right Christian doctrine.