Lake Turkana Potassium/Argon shenanigans:

1. According to Fitch & Miller 1970, (Nature) table 1, the first three samples taken from the layer above where KNM 1470 (homo rudolfensis) was found consistently dated to 220m years. Possible contamination from wall rocks was cited as the reason for the erroneous result and they continued with two other samples that gave a range of 2.3 to 4.6m years (table 2).
2. "Richard Leakey did not stand quietly by while all the pot shots were being taken at 1470 and the KBS tuff. He was disturbed enough by the rising tide of mammal-fossil evidence to ask Fitch and Miller to do another potassium-argon run. They did, and this time came up with a date of 2.4 million years. To the pig-fossil men this was a step in the right direction, but far too small a one; they felt that another dater should be tried. They were pleased when Thure Cerling, a University of California graduate student, turned up at the Berkeley campus with some samples of the KBS tuff that he had brought back with him from Lake Turkana. He gave the samples to Garniss Curtis, the acknowledged dean of potassium-argon dating and a pioneer in its application to Plio-Pleistocene fossils. Curtis ran tests on Cerling's samples, one of which returned a date of 1.8 million, the other a date of 1.6 million. Those were almost exactly what the pig-fossil men would have predicted, and they were delighted with them. ... For me the Curtis dates clinched it. There was no way that 1470 could be more than two million years old. I asked Jim Aronson not long ago what he could say about the 700,000-year swing between Fitch-Miller and Curtis. 'I think it has to do with the purity of the samples', he said. 'One of the first things Curtis and his group at Berkeley documented was that KBS sample they had been given was contaminated by a few grains of much older material. Since we are always operating on the outer fringe of the capability of the potassium-argon technique, accidental intrusions like this can loom very large--only a few grains can throw you way off. .... 'It's rather ironical,' said Aronson, 'that the KBS tuff is now probably the most reliably dated in all East Africa'", Donald Johansen, Lucy: The Beginnings of Humankind, 1990, pages 242-243

In other words, they kept taking samples until they found some that gave the results they wanted.

Potassium Argon:

1. In table 2 from 40Ar/36Ar Analyses of Historic Lava Flows (Earth and Planetary Science Letters, 1969) the authors show that 26 lava flows that solidified in the last 3500 years, 5 of them date > 130k years old, with two over a million years old. They also note, "The occurrence of excess 40Ar in the Hualalai flow is not surprising, because this flow is noted for its abundance and variety of ultramafic xenoliths. Naughton et al. and Funkhouser found ages as high as 3.0 × 10⁹ [3 billion] years for xenoliths from this flow and reported that fluid inclusions with a high 40Ar content are common in minerals in the xenoliths."

2. "The first analysis suggested an age of around 350,000 years, but later measurements suggested an age closer to 600,000 years. 'I think they got it right the first time,' says Stringer." Largest group of fossil humans are Neanderthals after all

Dinosaurs C14:

1. On this page you can see where 20 samples of acrocanthosaurus, allosaurus, hadrosaur, triceratops, and apatosaur were C14 dated at the University of Arizona using both the AMS and beta-decay methods to be between 22-40k years old. Authors Jean De Pontcharra and Marie Claire van Oosterwych have Ph.D's in physics and physical chemistry, respectively.  It was originally presented as a talk at the 2012 Western Pacific Geophysics Meeting in Singapore. Their paper was removed with the only explanation being "there is obviously an error in this data". You can see the rejection letter here. Here are before and after versions of the lists of papers at the conference. Note that #5 is missing in the after version.
2. Jack Horner was offered a $23k grant to C14 date his soft tissue bones, but declined.  He agreed the money was more than enough but wouldn't because it would give evidence to creationists.

Dinosaur Osteocytes, Collagen, DNA, etc:

1. "Here, we demonstrate that endogenous proteinaceous molecules are retained in a humerus from a Late Cretaceous [100-66 Ma] mosasaur (an extinct giant marine lizard). In situ immunofluorescence of demineralized bone extracts shows reactivity to antibodies raised against type I collagen, and amino acid analyses of soluble proteins extracted from the bone exhibit a composition indicative of structural proteins or their breakdown products. These data are corroborated by synchrotron radiation-based infrared microspectroscopic studies demonstrating that amino acid containing matter is located in bone matrix fibrils that express imprints of the characteristic 67 nm D-periodicity typical of collagen. Moreover, the fibrils differ significantly in spectral signature from those of potential modern bacterial contaminants, such as biofilms and collagen-like proteins. Thus, the preservation of primary soft tissues and biomolecules is not limited to large-sized bones buried in fluvial sandstone environments, but also occurs in relatively small-sized skeletal elements deposited in marine sediments. ... we find it reasonable to conclude that the collagenous biomolecules recovered from the fibrous tissues of IRSNB 1624 are primary. ... In order to remove absorbed carbonates and humic acids, a small bone sample (2 g) was pre-treated according to the acid-alkali-acid method; i.e., it was washed in 2% HCl solution at 80°C for 12 h, then in 5% NaOH solution at 80°C for 5 h, followed by a final wash in 2% HCl. After this procedure, the dried residues (258 mg) were combusted to CO2 using CuO as oxidizing agent. The CO2 was then mixed with H2 gas and reduced to elemental carbon before being analyzed at Lund University Radiocarbon Dating Laboratory using single stage accelerator mass spectrometry. Approximately 5 mg of carbon was produced, of which 3 mg was used in the analysis. ... Likewise, the amount of finite carbon was exceedingly small, corresponding to 4.68%±0.1 of modern 14C activity (yielding an age of 24 600 BP), and most likely reflect bacterial activity near the outer surface of the bone (although no bacterial proteins or hopanoids were detected, one bacterial DNA sequence was amplified by PCR, and microscopic clusters of bone-boring cyanobacteria were seen in places along the perimeter of the diaphyseal cortex).", Uvdal, Microspectroscopic Evidence of Cretaceous Bone Proteins, 2011

2. "These data are the first to support preservation of multiple proteins and to present multiple lines of evidence for material consistent with DNA in dinosaurs ... The most parsimonius explanation for all the data presented previously is that collagen is preserved in these ancient tissues. ... While ultimately, sequence data is required to verify the endogeneity of this material, it is unlikely that four independent assays, each capitalizing on different aspects of the chemistry of DNA, would show identical patterns of localization interior to these cellular structures, and different from antibodies to various proteins." Schweitzer, Molecular analyses of dinosaur osteocytes support the presence of endogenous molecules, Bone, 2013
3. This page is of questionable reliability but links to many more papers on soft-tissue finds:  http://kgov.com/dinosaur-soft-tissue

How long should biomolecules last?

1. According to table 1 in Biomolecules in fossil remains, (The Biochemist, 2002): At 0C the maximum survival time for DNA, collagen [a connective tissue protein] and osteolcin [a bone protein] are 125k, 2.7m, and 110m years, respectively. At 10C, the numbers drop to 17.5k, 180k, and 7.5m years.

2. "By analysing mitochondrial DNA (mtDNA) from 158 radiocarbon-dated bones of the extinct New Zealand moa, we confirm empirically a long-hypothesized exponential decay relationship. The average DNA half-life within this geographically constrained fossil assemblage was estimated to be 521 years for a 242 bp mtDNA sequence, corresponding to a per nucleotide fragmentation rate (k) of 5.50 × 10^-6 per year. With an effective burial temperature of 13.1°C, the rate is almost 400 times slower than predicted from published kinetic data of in vitro DNA depurination at pH 5. Although best described by an exponential model (R2 = 0.39), considerable sample-to-sample variance in DNA preservation could not be accounted for by geologic age. This variation likely derives from differences in taphonomy and bone diagenesis, which have confounded previous, less spatially constrained attempts to study DNA decay kinetics. Lastly, by calculating DNA fragmentation rates on Illumina HiSeq data, we show that nuclear DNA has degraded at least twice as fast as mtDNA. These results provide a baseline for predicting long-term DNA survival in bone.", The half-life of DNA in bone: measuring decay kinetics in 158 dated fossils, Proc. R. Soc. B, 2012

3. Summarized in NewScientist: "With an estimated burial temperature of 13 ºC, the DNA's half-life was 521 years – almost 400 times longer than expected from lab experiments at similar temperatures, says Allentoft. ... The oldest DNA to date belongs to insects and plants and was found in 450,000 to 800,000-year-old ice. Under subzero conditions, Allentoft and Bunce estimate that DNA's half-life can be up to 158,000 years, meaning the last remnants would disappear around the 6.8-million-year mark.", DNA's half-life identified using fossil bones

4. "Jeffrey Bada, an organic geochemist at the Scripps Institution of Oceanography in San Diego, cannot imagine soft tissue surviving millions of years. He says the cellular material Schweitzer found must be contamination from outside sources. Even if the T. rex had died in a colder, drier climate than Hell Creek, environmental radiation would have degraded its body, Bada says: 'Bones absorb uranium and thorium like crazy. You've got an internal dose that will wipe out biomolecules.'" http://discovermagazine.com/2006/apr/dinosaur-dna