Using SPI with 74HC595 and TPIC6B595

Arduino Nano and Arduino Mini both have the same processor - '328P.
Suggests a miswiring between the boards.
You also have a lot of extra stuff in your sketch that the SPI library takes of for you.
I've taken a shot at cleaning it up & left you some notes

#include <SPI.h>

// commented out a bunch of redundant code that SPI.h takes care of for you
// see comments also

//int pll_d=11; //piedino data
//int pll_c=13; //piedino clock
int pll_l=10; //piedino latch
//#define DATAOUT 11//MOSI
//#define DATAIN  12//MISO 
//#define SPICLOCK  13//SCK

void setup () {

  //missing for - add:
  pinMode(8, OUTPUT);

  //  pinMode(DATAOUT, OUTPUT);
  //  pinMode(DATAIN, INPUT);
  //  pinMode(SPICLOCK,OUTPUT);
  pinMode(pll_l, OUTPUT); 
  digitalWrite (pll_l, HIGH);  // may not be needed - SPI.begin may do this for you
  Serial.print("latch enable up");

  SPI.begin();  // move to end of setup?
  Serial.begin(9600);
  Serial.print("spi begin");
  //SPI.setDataMode(SPI_MODE0); // default - don't need
  //SPI.setBitOrder(MSBFIRST); // default - don't neeed
  SPI.setClockDivider(SPI_CLOCK_DIV128); // why so slow?  might as well use shiftout()
  // HC595 and TPIC6B595 work just fine at default speed (4 MHz)

  // digitalWrite(pll_l,LOW);
  // delayMicroseconds(1000);
  //Serial.print("latch enable down");
  //}


  //void loop(){
  //  digitalWrite(pll_l,HIGH);
  WriteADF(0x00, 0x58, 0x00, 0x05); //Reg5 
  delayMicroseconds(2500); // not needed - make sure shift registers have 0.1uF cap from Vcc pin to Gnd.
  WriteADF(0x00, 0x8c, 0x80, 0x3c); //Reg4
  delayMicroseconds(2500); // not needed
  WriteADF(0x00, 0x00 ,0x04, 0xb3); //Reg3
  delayMicroseconds(2500); // not needed
  WriteADF(0x00, 0x00, 0x4e, 0x42); //Reg2
  delayMicroseconds(2500); // not needed
  WriteADF(0x08, 0x00, 0x80, 0x09); //Reg1
  delayMicroseconds(2500); // not needed
  WriteADF(0x00, 0x3c, 0x00, 0x00); //Reg0
  //  SPI.end();  // don't need this unless you want to free D11-12-13 for other uses
} // end of setup

int WriteADF(byte a1, byte a2,byte a3,byte a4) { 
  SPI.transfer(a1);
  SPI.transfer(a2);
  SPI.transfer(a3);
  SPI.transfer(a4);
  Toggle();
  return 0; // not needed
}

void Toggle() {
  digitalWrite(pll_l,HIGH);
  delayMicroseconds(1);
  digitalWrite(pll_l,LOW);  // this leaves SS pin low - normally it is left high after SPI.transfer
  // try swapping these around
}

void loop(){
  digitalWrite(8,HIGH);
  delay(2000);
  digitalWrite(8,LOW);
  delay(2000);
}