There's a difference between controls done to genuinely test your hypothesis and those done when you just want to show that your hypothesis is true. The authors have done some of the latter, but not the former. They should have mixed pregrown E. coli or other cells with the arsenate supplemented medium and then done the same purifications. They should have thoroughly washed their DNA preps (a column cleanup is ridiculously easy), and maybe incubated it with phosphate buffer to displace any associated arsenate before doing the elemental analysis. They should have mixed E. coli DNA with arsenate and then gel-purified it. They should have tested whether their arsenic-containing DNA could be used as a template by normal DNA polymerases. They should have noticed all the discrepancies in their data and done experiments to find the causes.
I'm no microbiologist, but I read the paper carefully because it seemed to be such an interesting result if true. And the paper simply does not include the controls to show that arsenate has been taken up as part of the DNA. All the other claims in the press accounts of the discovery -- for example, the idea that the organisms could substitute arsenate for phosphate in ATP -- were complete fiction.
I really appreciate being able to read the informed opinion of Redfield, whose lab specializes in the take-up of exogenous DNA by microorganisms. She writes that if a student had come up with the same results, she would have sent him "back to the bench" to confirm with more controls.