Interested in using an ADC to build a high resolution voltmeter. Any experience using the MCP3421 ADC?
This doesn't answer your question, but have you looked into the AD737?
You don't need a fast A/D for a voltmeter you need something slow (3 or 4 conversions per second) but much more accurate.
Try looking at the ICL7660, that is a four and a half digit DVM using the dual ramp conversion method.
The closest I could find is the ICL7135, but that doesn't need an Arduino...
A quick look at the data sheet looks like it is much the same.
but that doesn't need an Arduino
Just to be a DVM no, but you can put an arduino on the end to catch the multiplexed BCD outputs and then you have a voltmeter that you can do thing with the readings, like log them, pass them on to processing, light up LEDs on pass / fail readings.
If you just want a DVM and just want to display the results with and arduino, then take the dual ramp part of things (as described in the data sheet), make your own using an op amp, and use the arduino to time the charge / discharge cycles. This is much the best way to get accuracy than going for an N bit A/D that can sample fast.
There are inexpensive DVM meters available these days that have a serial data output for logging readings.
Left
Yes but not as inexpensive as this chip. 
Would the MAX1204 be suitable for this kind of thing? Looks simpler to implement, and has an SPI output.
That ADC has 10 bit resolution which is the same as the Arduino analog pins. I was thinking about a Microchip ADC with 22 bit resolution which can be used to build 6-digits DMMs. Probably way overkill but only 3 bucks. The application I was thinking was to sort/match resistors for Audio/Hi-Fi applications.
4.5 digit DMMs can be bought for $40, but 6 digits are very expensive