Brandolini's law is strong in this one.
Let me pick one thing: their main (we-found-alien-life-level) claim that they detected vaccine-derived mRNA and non-functional fragments of the artificial plasmid DNA used in vaccine manufacturing in this person's circulating cells, 3+ years after vaccination. This DNA is supposed to be carefully filtered out BTW before packaging into vaccines, but OK, it's worth thinking about. This DNA would also be degraded quickly if injected - it's linearized before use, but OK let's say multiple processes failed somehow, and some voodoo magic keeps it from being gobbled up. Even they don't outright claim to know how it got there, because any concrete proposed mechanism would either sound extremely implausible or impossible - as it turns out it probably doesn't matter either way (see below.)
On p. 16 of the paper they claim to detect the actual vaccine mRNA only in exosomes. They could not detect it at all in peripheral blood mononuclear cells, where, even more extraordinarily they claim to have found and sequenced the ori1 and ori2 plasmid backbone used in Pfizer vaccine manufacturing (but crucially, none of the three spike protein sequences that would actually cause immune system problems if transcribed into a protein.) So I don't know what to make of the ori1/2 artifacts, except that I'd check that these sequences were truly unique to the Pfizer process (often these are conserved sequences that many labs use.) Even if they are somehow from the vaccine, and somehow active, they lack the spike sequences so would not produce mRNA in exosomes and thus spike proteins (so irrelevant to their other measurements of spike protein.)
So where do they think the mRNA in the exosomes come from? Well, if it ISN'T in the PBMC's (which it would be if it was being expressed there), then it has to be in "extracellular vessels" from the original injections. For 3+ years. At detectable concentrations. Mmmm hmmm. They could check this of course because the Pfizer vaccines use specially modified RNA's - that would be a smoking gun, but of course they didn't check this. You know why. You know where else one gets mRNA for spike proteins, that could end up in exosomes? Covid. Or maybe just a recent vaccine injection. Interestingly, they didn't bother to sequence the amplicons of the mRNA that they banded out on a gel - that also would be a pretty convincing indication it was from Pfizer, as any Covid in the wild today would have enough mutations to be identifiable. They did this exact thing for the ori1/2 bands, hmm I wonder why they didn't do this? You know why.
I could go on, but I have done enough public service for one morning.