Another good starter would be to check the refences cited, and note the rather high number about whose results this article is entirely dishonest.
More just responding directly to them from what I know (note: I am a paleontologist and do not claim to be an expert on other topics)
1: Density waves are quite a simple explanation: if you have a collection of elliptical orbits with lots of bodies on them which are very slowly precessing (which they always do because of gravitational effects), then you will get spiral arms of star formation, due to the denser gas clouds in that region. M51 has been known to have detailed spiral structures for over a century, and it has a large satellite galaxy, which seems to correlate strongly with having the elliptical orbits needed for pretty spirals.
2: More like one every 100 years. They get very hard to see after a few tens of thousands of years, also “potentially visible within 200 ly of us” is not the same as “actually visible within 15,000 ly of us, with lots of dust and gas in the way”, also there haven’t been any visible supernovae in our galaxy in the last 350 years, suggesting that many of those which happen aren’t visible to us. A counter-point to this is the fact that there are a few thousand known pulsars, which have been directly observed forming from supernovae, and given the output angle, there are probably more like 50,000 pulsars in our galaxy.
3: We can’t directly observe the Oort cloud, but we can tell that there are a number of comets far outside the visible range of our telescopes: many go past the sun once every 10-100,000 years (Hyakutake, e.g.). Interactions with giant planets are all but guaranteed. Whether those interactions make a significant different to a body’s orbit varies. Also, the Kuiper Belt is just supplying the shorter-period comets (<1000 year orbits).
4: Quote from the abstract of one of the articles cited: “Prior to widespread farming and deforestation (beginning 2000-2500 yr ago), however, sediment discharge probably was less than half the present level.” The article from which they get the subduction rate is only looking at deep ocean, not continental shelves or slope. A realistic estimate for building up the sediment in the deep ocean is more like 200,000,000, which is about the lifespan of oceanic crust.
5: Summary table of mean ocean concentrations and residence times | MBARI
Applying this same method to the concentration of Tin, the oceans must be only 5 years old. Applying this to Bromine, the oceans are 130,000,000 years old. Neither of those is remotely consistent with 6,000 years, or with each other.
6: The decay rate ignores current data, which gives a much more complicated picture. This is also a self-defeating argument, in that the ability to have the magnetic field flip every few hours makes any extrapolation impossible.
7: The layers did crack. Also those bends are dozens of feet across. If the layers were still “wet and unsolidified”, then they wouldn’t be discreet layers.
8: DNA cannot survive in good condition in typical conditions more that a few 10s of thousands of years. The permafrost that the Neanderthals were found in is near-ideal conditions: very cold and dry. The insects in amber and dinosaurs have tiny pieces of “we can tell this used to be a bit of DNA”. The soft tissue in question is collagen, which is about as sturdy as you can get without being ossified. Clam ligaments have been known for well over a century from the Carboniferous. That bacterium was in a brine inclusion within a salt crystal, which is a near-optimal environment for preserving DNA.
9: Those deposits are hydrothermically altered, hence dates on them are not reliable. Being able to tell what source atom was present is quite tricky. Also, for any of these to be valid, radiometric decay rates cannot change, as that would make all extrapolations useless (not to mention it would destroy every atom larger than hydrogen) If the author is saying that the lack of 218Po is a problem (ambiguous which isotope), then that is either a typo, or the writer is seriously confused, given that the half-life of 218Po is 3.1 minutes and the longest half-life in its decay chain (by a factor of 40) is 22.2 years (for 210Pb) (FYI, 218Po is in the 238U decay chain).
10: Pressure makes a significant difference to rate of leaking. Also, the rate is based on two data points specifically selected to give the “right” age.
11: ELIMINATING ALL CONTAMINATION IS IMPOSSIBLE. 5x10^-6 and 0 are identical when the margin of error is 0.001.
12: A lot of that time was spent in warm, wet climates, which promotes decay. Also, we haven’t dug holes to look for human remains everywhere, for obvious reasons.
13: There is a difference between “knowing plants grow from seeds” and “knowing how to create a field dedicated to growing one specific crop”. There is also the point that even if someone knows how to do something difficult, they probably won’t without good reason: if hunting and gathering takes less effort than farming and produces more food, which one would you do?
14: Literacy requires people to have enough free time to learn a written language. This again ignores the “why bother?” aspect: if you don’t have a need to make written records (which were usually for things like tax collection), you probably won’t.