Last Night's Viewing: Death Row, Channel 4<br />Get Your House in Order, Channel 4

"What we are doing here is not an instrument for proving your innocence," Werner Herzog told Hank Skinner at the beginning of Death Row. Hank's innocence, it should be said, is a fiercely contested matter. Hank and his lawyers strenuously assert it, but the state of Texas, which aims to execute Hank just as soon as they can get the final paperwork sorted, is stubbornly resistant to the idea that they got the wrong man for the 1995 murder of Twila Busby and her two mentally disabled sons. Anyway, Herzog was as good as his word. This gripping film offered very little evidence that cast doubt on Hank's original conviction. What it did do was confirm once again the strange and wonderful innocence of Werner Herzog.

I don't mean by this that he's a stupid film-maker, just that he's managed to preserve into maturity a quality of almost childlike earnestness. There's no hidden agenda or concealment in the way that he addresses the world, and no sense that he will trim his delivery to match the audience. He can sit face to face with a convicted killer and ask him, in tones of urgent gravity, "How does time function? Does it stand still or does it race? Tell me about time." Hank Skinner, it has to be said, was more than up to the task of replying in kind – a garrulous autodidact who was prone to quoting Leonardo da Vinci or suddenly alluding to the epic of Gilgamesh. Not every death row inmate can have quite such a Herzogian breadth of reference.

The first of three interviews with death row inmates, this one began with Hank's account of the time that he got within 20 minutes of execution. He'd made the 40-mile journey from death row to the specialist execution centre, and he'd started on his last meal – a gargantuan feast of fried chicken, catfish fillets, bacon-cheese burger, grated cheese, bacon bits, large fries and chocolate milk. Then he called his lawyer, who told him he'd just received a stay of execution. "I felt like somebody had lifted a 1,000lb weight off my chest," said Hank. And then the warder explained that the defence lawyer's word wasn't enough. Unless the governor or attorney called, the execution would go ahead. "That was the longest 23 minutes of my life," Hank said of the gap between his first call and the official confirmation.

It did occur to you that if the Texas Department of Corrections simply let Hank eat what he wanted, he'd soon do the job for them. And if that sounds improperly flippant, all I can say is that Hank himself had an eye for the black comedy of his situation. Why hadn't he taken his blood pressure medication, a guard asked him when this last minute reprieve gave him palpitations. "Well, hell, they were going to kill me!" Hank replied, "What's the point?" He then insisted on finishing off his last meal before he was taken back to death row. As if he wanted to counterbalance the unexpected charm of Hank's presence, Herzog broke off from claustrophobic face-to-face through the glass to tread the location of his crime, a grim tract of Texas hardscrabble under a sky like the end of the world. And then, after more conversation, he finished by driving the route Hank may yet follow in one direction only, offering a premonition of his subject's final sights. The last image of the film was a giant crab wearing sunglasses outside a seafood restaurant – mad, and innocent, and pure Herzog.

Get Your House in Order bizarrely marries the hoarding documentary genre with a makeover show, pairing an antiques dealer with an interior designer, who uses the proceeds of the clutter sale to fund a redecoration. Judging from last night's show about a shopaholic called Abi, they could do with a resident psychiatrist too. Death please, and no reprieve.