I've recently looked at the AD5696 (quad 16 bit 0->2.5V output DAC) and the data sheet tells you this: -
- INL and DNL add up to +/- 4 LSBs (+/-0.15 mV error in 2.5V full scale)
- Zero offset is +/- 1.5 mV (2.5 volts FSR)
- Gain error is +/- 0.1% of FSR (1.25 mV in 1.25V mid scale)
Total "mid-scale" error when extended to 10V full scale is 0.60 mV + 6 mV + 5 mV = 11.6 mV but this assumes a perfect amplifier following the DAC with perfect resistors. 0.1% resistors could give you an extra gain error of 0.2% but, MAXIM produce accurate and temperature stable potential dividers that are ratiometrically 0.025% so I'd consider them.
Also, as has been said in comments the voltage reference is paramount. You can get a voltage ref of initial accuracy 0.02% but of course this adds an error. Can you live with this unadjusted error?
Temperature and long-time drift account for significant errors. If you have a situation where the DAC is subjected to several degrees change in temperature then you have to look at the ppm/degC the gain might shift - the device above is +/- 1ppm/deg C so it's pretty good BUT you must still consider the error.
Ditto for the voltage reference - I am considering using the LTC6655 - it has an initial accuracy of 0.025% (which I will adjust) and a temperature stability of 2ppm/degC (max).
One final note if using a single supply DAC, check what the zero value eror is - this tells you how close to 0C the DAC will work - you might find that the bottom 5mV of range (or the top 5mV of range) are deadbands and unusable.