Creationists are dimly aware that the fossil record exhibits order, although (as we shall see) they don't really know what this order consists of. In the creationist imagination, the fossil record has crude, primitive organisms at the bottom, and then as one works up through the sedimentary layers the organisms get progressively more sophisticated, complex, agile, intelligent, etc, culminating in the awesome wonder that is Man.
To explain this imaginary fossil record, they have produced some imaginary mechanisms.
The first mechanism ("differential mobility") involves creatures running uphill to escape the Flood. Those with superior speed, intelligence, stamina, etc, were able to make it higher up the antediluvian hills before perishing, thus sorting them as (creationists suppose) they are sorted.
You will note that for the sorting so produced to be consistent, the race must always be fair: that is, every animal must start the same distance from the top of the nearest hill. For clearly if some slow cumbersome brute were to cheat by starting off near or at the top of the hill, it would arrive at the summit while its more gifted competitors were drowning lower down its slopes. Or if a fast wily animal such as a cheetah started a long way from the nearest hill, then it might drown and be buried in Flood sediments while a slower but more opportunely placed Triceratops, having started on or near the lower slopes of the hill, was still determinedly plodding upwards.
How this exquisite fairness was arranged, no creationist is prepared to explain.
You will also note that the hills need to be more or less of a height. For consider: if on one hill the dinosaurs only make it halfway up, whereas the modern mammals gain the summit, then what will be the result when animals take refuge on a different hill which is only half the height? Would not the dinosaurs and the modern mammals end up in the same strata, contrary to observation?
Still, this is perhaps a minor quibble, since there is nothing to stop creationists imagining that all the antediluvian hills were in fact the same height. They have imagined much, much sillier things to plug the holes in their hypotheses.
A more serious objection is our inability to find the hills. In the creationist scenario, we would have a hill containing no fossils and presumably consisting of igneous rock, covered over with sedimentary rock (the sediments being deposited by the Flood) with the fossils distributed on the former surface of the hill. But this is not what we find.
We might also object that we do not in fact find fossil organisms sorted according to their speed and agility. For example, it is not really conceivable to suppose that a predator such as Gorgonops could have been outrun by a three-toed sloth, and absurd to think that it could have been outrun by an oak tree. Real geologists attribute its position in the strata to the fact that it lived in the Permian; "Flood geologists" have a more difficult task.
So creationists also drag in a second mechanism, "hydrological sorting" (which real scientists usually call "hydraulic sorting"). Objects in an agitated fluid (such as the raging waters of the flood) will tend to be sorted according to characteristics such as shape and density, and this is supposed to explain why (for example) velociraptors end up in one set of strata while gorgonopsids end up in another.
One objection that immediately occurs is that the sediment in the geological record is certainly not hydraulically sorted: if it was, all the larger particles would be at the bottom, and the geological record would grade up from conglomerate to sandstone to mudstone and limestone. This is not what we observe. We should like to hear any explanation of how the fossils got to be hydraulically sorted but not the sediments in which they lie.
We might also reason like this. If hydrological sorting gives us (let us say) a velociraptor buried in sandstone, then it must have the same hydraulic properties as sand. This sounds a little improbable, but let it pass. Now, if we also find (let us say) a gorgonopsid buried in sandstone, then it too must have the same hydraulic properties as sand.
But in that case do we not have to conclude that a velociraptor has the same hydraulic properties as a gorgonopsid? So why are they never found buried in the same strata together?
Some objections may be raised against both mechanisms equally. For example, we can find in the same strata a given species of dinosaur, their young, their nests, their eggs, and their footprints. Are we to suppose that the eggs ran uphill just as fast as the adult dinosaurs did? Or that it just so happened that the eggs of a given species always have just the same hydraulic properties as the adults that lay them? (Footprints, of course, cannot be transported by water at all.)
The third mechanism ("ecological zoning") is explained as follows by the creationist Henry Morris: "Marine invertebrates would normally be found in the bottom rocks of any local geologic column, since they live on the sea bottom. Marine vertebrates (fishes) would be found in higher rocks than the bottom-dwelling invertebrates. They live at higher elevations and also could escape burial longer. Amphibians and reptiles would tend to be found at still higher elevations, in the commingled sediments at the interface between land and water [...] Mammals and bird would be found in general at higher elevations."
One obvious objection is that these ecological zones would necessarily differ not just in altitude but also in location: they cannot be stacked one on top of another like different floors in an apartment complex, with the mammals living over the reptiles, and the reptiles above the fish. But in the fossil record we do find land animals and other clear indications of a terrestrial habitat directly above marine fossils and sediments.
What is more, we find the reverse, in locations which have undergone multiple transgressions and regressions of the sea. So for example in the rocks of the Grand Canyon not only do we have terrestrial formations with terrestrial fossils sitting directly on top of the marine Redwall Limestone, but also we have the marine Kaibab Limestone sitting directly above these terrestrial formations.
This leads us on to the fundamental creationist blunder which we mentioned at the start of this discussion: they have not the faintest idea what the fossil record looks like, and so are contriving their explanations for something that isn't actually there.
It is not hard to discover the roots of their confusion. They have grasped one fact about the fossil record: that it upholds the theory of evolution, and that they need to explain this away. Given this premise, they have deduced what the fossil record must look like (rather than actually looking at it, which would involve work). And since they do not know what the theory of evolution is, or what data would support it, their deductions are entirely at odds with what the fossil record looks like.
For what they seem to expect is that the fossil record should be a recapitulation of the medieval concept of the Great Chain of Being: invertebrates on the bottom, then the fish, then the amphibians, the reptiles, and finally the mammals in all their glory. To quote Morris again: "These higher animals (land vertebrates) would tend to be found segregated vertically in the column in order of size and complexity [...] The general order from simple to complex in the fossil record, considered by evolutionists to be the main proof of evolution [yes, Morris actually wrote that!] is thus likewise predicted by the rival theory ..."
But evolution is not in fact the story of the Great Chain of Being, but of the branching of the Tree of Life; and five seconds' thought would have told the creationists what the theory of evolution does actually predict. For, obviously, we expect any group of organisms to persist in the fossil record until it actually goes extinct. And invertebrates, fish, amphibians, and reptiles have not gone extinct. So we would expect to find (for example) lizards in the most recent sedimentary rocks, because they are still with us: whereas apparently Morris would expect them to be absent because they are small, simple, primitive, lower down the Great Chain of Being; we would expect to find small invertebrates alongside large mammals, not in the least "segregated in order of size and complexity"; we would expect to find fish in the most modern sedimentary rocks, so long as the sediments are marine; since tortoises are still alive, we expect to find them in more recent strata than animals which are larger, faster, and extinct; and so on and so forth. And this is what we do find.
We have, therefore, the creationists' own assurance that their model of the formation of the fossil record predicts and explains features of the fossil record which it flagrantly, blatantly, does not exhibit. And this in itself is sufficient to destroy their model.
We should not anticipate that any creationist will ever explain the actual features of the fossil record in terms of the Flood. It is unlikely at this late date that any of them is going to find out what the fossil record looks like, an activity which would both contradict their prejudices and involve doing some actual work. But I invite any creationist who wants to to give it a try.
And of course anyone else is free to point out problems with the creationist model as it stands. I can think of several more, but this post has gone on long enough ... and the horse is dead.