Measuring AC voltage (0.333vac max) using a 10 bit ADC on Atmel ATMEGA328

A few thoughts:

I'm assuming the PSU is DC within the range of 0V - 30V. (i.e no negative or AC voltages)

I don't know much about Arduinos, but do you have to set the pin to an analogue input? (e.g. like you would have to an a PIC) I'm thinking maybe the analogRead routine takes care of it. Also is the ADC reference voltage set correctly? (I notice there is a Aref pin floating on your schematic)

EDIT - Aref pin:

Atmel say:

The reference voltage for the ADC (VREF ) indicates the conversion range for the ADC. Single ended channels that exceed VREF will result in codes close to 0x3FF. VREF can be selected as either AVCC , internal 2.56V reference, or external AREF pin. AVCC is connected to the ADC through a passive switch. The internal 2.56V reference is generated from the internal bandgap reference (VBG) through an internal amplifier. In either case, the external AREF pin is directly connected to the ADC, and the reference voltage can be made more immune to noise by connecting a capacitor between the AREF pin and ground. VREF can also be measured at the AREF pin with a high impedant voltmeter. Note that VREF is a high impedant source, and only a capacitive load should be connected in a system. If the user has a fixed voltage source connected to the AREF pin, the user may not use the other reference voltage options in the application, as they will be shorted to the external voltage. If no external voltage is applied to the AREF pin, the user may switch between AVCC and 2.56V as reference selection. The first ADC conversion result after switching reference voltage source may be inaccurate, and the user is advised to discard this result.

So if the external reference is selected you need to apply a voltage to it. From your comment below it looks like this may be the case. Try connecting it to AVcc (or whatever you want the top of the ADC range to be)
You can optionally add a 100nF cap to ground to reduce noise if necessary also.

Is your 5V supply stable? Have you got bypass caps present? (mentioned but not acutally shown on schematic)

Is your PSU sharing ground with the Arduino? If not this could cause the issues you are seeing.

The offset with the zener is of little use. The best zeners have a 1 % tolerance, which is 100 mV for a 10 V zener. On a 10-bit ADC this is a 20 count error, on a 12-bit ADC an 82 count error. You could trim the error away if you can measure the voltage accurately enough, but there are other factors. The BZX84-A10 has an 8 mV/°C temperature coefficient, giving a 2 count error per °C change in temperature for the 10-bit ADC, and 7 counts for the 12-bit. Looks like it's better suited as thermometer than as voltage meter. When you use a 10 V zener you'll also need a higher voltage power supply.

The resistance divider will do much better. Resistors also have a tolerance, but at 25 ¢ a 0.1 % resistor is still affordable. (Better that 0.1 % becomes expensive quickly: a 0.05 % costs almost 1 dollar.) At 10-bit resolution that will give you a 1 count error, 4 counts at 12-bit. Temperature coefficient will be less of a problem if both resistors are from the same series and placed close to each other: since the divider is ratiometric resistance changes will cancel each other out.

The numbers indicate that a higher than 10-bit resolution is of little use; component tolerances and variations will cause extra bit to be unreliable. A few extra bits may help to increase noise immunity, though, by averaging a series of measurements, or using a sigma-delta ADC, which averages the input signal anyway.

There's also something more philosophical: we always want better, but why on earth would you want to know a 12 V battery's voltage to a precision of better than 10 mV. You'll have a hard time getting the required resolution, and you'll always be uncertain about that last digit.

The ADS1000 is a low cost 12-bit ADC which will operate from a single 5 V supply.