A. Biblical Problems
First, the YEC claim that the fossil record is mostly the result of Noah's flood actually stands in direct contradiction to what the Bible says. This is because such a belief requires the garden of Eden to predate the fossil record. This in turn is problematic because the Bible locates the four rivers associated with the garden of Eden on the surface of the earth--on top of the fossil record--not five miles underground where Paleozoic rocks occur in the Middle East (a fact known from extensive drilling).
Most YECs seems blithely unaware of this problem and those YECs who are aware try to explain away this inconvenient truth by claiming the Tigris and Euphrates rivers associated with the garden of Eden in Genesis 2 are not the same rivers as the Tigris and Euphrates Rivers in the Middle East, but entirely different rivers that just happen to have the same name. But the problem with that theory is that it's not supported by the Bible and actually contradicts and runs counter to the Bible that YECs say they believe in and take literally. For example, Genesis 2:14 directly identifies the Tigris River as the river which 'flows east of Assyria', the same river we know today as the Tigris River and the identification with Assyria shows the river still existed (on the surface of the earth) 'post-flood' (instead of being buried five miles underground below the Paleozoic). Same thing with the Euphrates River, which is mentioned in Genesis 2 but also again in Genesis 15:18 with the Abrahamic covenant when Yahweh tells Abraham the land of his descendants will extend from Egypt to the great river Euphrates that is still so-named today.
Thus, given Mosaic authorship of Genesis, Moses understood the Tigris and Euphrates Rivers associated with the garden of Eden as the same Tigris and Euphrates known in his time and known to us today.
Thus, what the Bible teaches stands in direct contradiction to YEC flood geologists who insist that most of the fossil record was put down in Noah's flood. It is also difficult to reconcile with those who insist there was no death of any kind before 'the fall', since that too would require the garden of Eden to predate all the death in the fossil record.
Saying (1) the Bible presents Noah's flood as universal/global/cosmic in extent, and (2) the fossil record is primarily the result of Noah's flood, are two completely different claims. Claim #1 is true. The Bible does, in fact, depict Noah's flood as not merely global in extent but in almost cosmic proportions as a reversal of creation itself and a regression from order back to a pre-creation chaotic state where the 'waters above' and 'below' are no longer separated as they are on Day 2 of the Genesis creation account. Now whether this is meant to be taken literally or is hyperbole and purposeful exaggeration to make a theological point is a separate matter of debate. Either way, Genesis does not depict Noah's flood as a local flood, but as a global, universal catastrophe on an epic, cosmic scale.
That said, however, the Bible does not equate the fossil record with Noah's flood. The Bible doesn't even mention the fossil record, so claim #2 is an assumption that YECs often make without critical assessment. This distinction is important to avoid potential misunderstanding, because this OP is not disputing claim #1, only claim #2. That is, it is not the Bible's depiction of Noah's flood that is being disputed, it is only the unfounded YEC assertion that the fossil record is mostly the result of Noah's flood that is being disputed.
This topic is of further importance because YECs commonly maintain that 'flood geology' is just a different, equally valid interpretation of the *same data* used by modern geologists. But this is simply untrue. 'Flood geology' is not an equally valid interpretation of the 'same data', but a forced interpretation based on isolated, cherry-picked examples that ignore a mountain of incongruous data to the contrary.
There are, in fact, biblical and scientific problems with the YEC claim that the fossil record is mostly the result of Noah's flood. The purpose of this OP, then, is to present some of these problems, while welcoming anyone who disagrees to present their case for claim #2.