One point not yet mentioned is switched capacitance on the input. Many ADCs will connect a capacitor to the input while they take a measurement and then disconnect it sometime later. The initial state of this cap may be the last voltage measured, VSS, or something inconsistent. For accurate measurement, it is necessary that the input either not budge when the capacitance is connected, or that it bounce and recover before the capacitor is disconnected; in practice, this means that either the capacitance on the input must be above a certain value, or else that the RC time formed by the input capacitance and source impedance must be below a certain value.
Suppose, for example, that the switched input capacitance is 10pF, and the acquisition time is 10uS. If the input impedance is 100K, there is no input capacitance other than the capacitance of the ADC, and the difference between the starting cap voltage and the voltage to be measured is R, then the RC time constant will be 1uS (10pF * 100K), so the acquisition time will be 10 RC time constants, and the error will be R/exp(10) (about R/22,000). If R might be the full-scale voltage, then the error will be a problem for 16-bit measurements, but not for 12-bit measurements.
Suppose there were 10pF of capacitance on the board in addition to the 10pF of switched capacitance. In that case, initial error would be cut in half, but the RC time constant would be doubled. Consequently, the error would be R/2/exp(5) (about R/300). Barely good enough for 8-bit measurement.
Increase the capacitance a little more and things get even worse. Push the capacitance to 90pF and the error would be R/10/exp(1) (about R/27). On the other hand, if the cap gets much bigger than that, the error will go back down. With a capacitance of 1000pF, the error would be about R/110; at 10,000pF (0.01uF), it would be about R/1000. At 0.1uF, it would be about R/10,000, and at 1uF, it would be about R/100,000.