| Well, they were not a problem to explain in the 19th century, and are still not a problem now.
These fossils are reasonably common, and have been mentioned in the scientific literature for well over a century, under the name upright fossils or in situ trees. No well-read geologist finds them surprising, and no geologist has ever claimed that it took millions (or even thousands) of years to bury them. Science is perfectly happy with the idea that deposition is occasionally rapid.
Geologists agree that the numerous upright fossils couldn't have all been buried at the same time.
Big trees commonly stay upright for years and even decades after death. Some "drowned" trees can even keep living, if they are tolerant of waterlogged conditions. For example, at Reelfoot Lake in Tennessee, there are some bald cypress trees that have kept growing in the lake since an earthquake submerged them in 1812.
Some upright fossils had rotted-away interiors by the time their burial was final. So, in those cases, the tree had stood dead for some time. The typical height of upright fossils is on the order of two meters, so many of these fossils represent only the base of the original tree. The top of the tree presumably rotted.
In the present day, deposition just like this can be done by floods, by natural levee breaches, and by course changes of river channels. Such floods often repeat themselves several times per decade, particularly in a basin area which is sinking. Each repetition would leave one layer.
All known upright fossils were buried in days, a year or so, or else periodically across perhaps a few decades. They occur all over the world, because swamps, river deltas and volcanoes also occur all over the world.
One singl (biblical) flood could not have caused these "polystrate" fossils.
The first argument is that the fossils aren't all found on one single level of the Geologic Column. Some are from the Devonian Period, well before the dinosaurs. Some were buried long after the dinosaurs went extinct. This is what you would expect if each burial was caused by a small, local event. And, there are differences, depending on where they are found. For example, giant lycopod trees are only found in Carboniferous Period rocks, and cypress trees aren't found below the Cretaceous Period. The same comment applies to their leaves and spores and pollen. But this is exactly what you would not expect if a single, global flood had washed over them. Surely the flood would have ripped many trees up, and dropped them elsewhere. Or if not the trees, at least the pollen.
The second argument is that some upright fossils were transported to where they are now. Others are clearly still in place (in situ), because they are still rooted into a fossilized soil. The transported trees have had their root systems ripped, but the in situ trees still have the small, fine rootlets in place. It does not seem possible for a single global event to transport some trees and not others.
The third argument is that there are some upright trees which are on top of other upright trees. We know that the upper tree grew after the lower one was buried, because the uppper tree is clearly in situ.
An example of this is a burrow pit near Donaldsonville, LA. When they excavated backswamp clays to rebuild the adjacent levee, they uncovered three levels of upright cypress forests buried on top of each other beneath the recent floodplain. These polystrate trees are buried within recent Mississippi River deposits that are only 4,000 years old. The much older upright trees in Yellowstone Park are similarly layered.
So you see, it poses absolutely NO problem for geology or paleontology.  | 
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