while((ADC->ADC_ISR & 0xC0)==0);// wait for two conversions (pin A0[7] and A1[6])
Well spotted - what it should actually be is this:
while((ADC->ADC_ISR & 0xC0)!=0xC0);// wait for two conversions (pin A0[7] and A1[6])
I'll go back and change my code in case anyone else copy/pastes it.
For reducing missed samples and allowing more processing time in the main loop, the biggest win comes through using peripheral DMA. This example uses DMA and interrupts - although if you are new to the Due, don't expect to understand it all at once 
#undef HID_ENABLED
// Arduino Due ADC->DMA->USB 1MSPS
// by stimmer
// Input: Analog in A0
// Output: Raw stream of uint16_t in range 0-4095 on Native USB Serial/ACM
// on linux, to stop the OS cooking your data:
// stty -F /dev/ttyACM0 raw -iexten -echo -echoe -echok -echoctl -echoke -onlcr
volatile int bufn,obufn;
uint16_t buf[4][256]; // 4 buffers of 256 readings
void ADC_Handler(){ // move DMA pointers to next buffer
int f=ADC->ADC_ISR;
if (f&(1<<27)){
bufn=(bufn+1)&3;
ADC->ADC_RNPR=(uint32_t)buf[bufn];
ADC->ADC_RNCR=256;
}
}
void setup(){
SerialUSB.begin(0);
while(!SerialUSB);
pmc_enable_periph_clk(ID_ADC);
adc_init(ADC, SystemCoreClock, ADC_FREQ_MAX, ADC_STARTUP_FAST);
ADC->ADC_MR |=0x80; // free running
ADC->ADC_CHER=0x80;
NVIC_EnableIRQ(ADC_IRQn);
ADC->ADC_IDR=~(1<<27);
ADC->ADC_IER=1<<27;
ADC->ADC_RPR=(uint32_t)buf[0]; // DMA buffer
ADC->ADC_RCR=256;
ADC->ADC_RNPR=(uint32_t)buf[1]; // next DMA buffer
ADC->ADC_RNCR=256;
bufn=obufn=1;
ADC->ADC_PTCR=1;
ADC->ADC_CR=2;
}
void loop(){
while(obufn==bufn); // wait for buffer to be full
SerialUSB.write((uint8_t *)buf[obufn],512); // send it - 512 bytes = 256 uint16_t
obufn=(obufn+1)&3;
}
It reads ADC data at 1 million samples/sec and outputs the data to SerialUSB. (I've only tested it on Linux and most of the time it works, sometimes it is unreliable, I don't know why). Using GNU Radio I was then able to analyse the data stream and receive a long-wave radio signal, with an LC tuned circuit into A0 as an aerial.
