Problems reading an analog input and output with 12 bits resolution

There are still some issues with the ADC and DAC.
I found and reported earlier, that the ADC readings drop as soon the ARM is warming up a bit (>32*C).
The DAC is obviously outputting voltages only in the range of 1/6..5/6 of 3300mV -
see also postings at: http://arduino.cc/forum/index.php/topic,129765.15.html
I have modified your code as follows which should work with above limitations:

/*
Read the value of the potentiometer (1.000V) at A0 and multiply
for 1.625 and output it at DAC1 both with 12 bits resolution 
*/
unsigned long val = 0; // variable to store the value coming from A0
unsigned long val2 = 0;
unsigned long outputValue =0;
int analogInPin = 0; // Analog input pin connected to the variable resistor
void setup()
{
  analogReadResolution(12); //read-resolution to be set first
  analogWriteResolution(12); //this should not apply according to documentation but surprisingly does not show up as error?
}
void loop() {
  val = analogRead(analogInPin); // read the voltage on the pot
  val2=val*1625/1000; //recommended and faster to use integers instead of float for calculations.
  outputValue = map(val2,550,2750,0,3300); //to normalize limited output range
  analogWrite(DAC1,outputValue); //write at DAC1
  delay(500);
}