I really think that it's difficult to make generalized statements, because there are so make different DAC's available. DAC's can introduce audible errors, some may be obvious, like a portable CD player having more background noise than a separate CD player. Other errors may be fairly subtle, and require careful subjective and objective testing to establish -
'Fielder has presented an objective technique suitable for evaluating the audibility of nonlinearity produced by digital converters. In [1] it is shown that noise and adjacent signal masking effects can often ameliorate nonlinearities, but that high-level tests show that seemingly small discontinuities can be quite audible under the right circumstances". In the absence of an exact requirement for inaudibility of distortion, a tight overall specification must be sought.'
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http://www.ee.usyd.edu.au/~jimr/pubs/papers/aes97.pdf
Rathmell, J. et al. (1997) "TDFD-based Measurement of Analog-to-Digital Converter Nonlinearity", Journal of the Audio Engineering Society, Volume 45, Number 10, pp. 832-840; October 1997.
One thing that has recently been discussed a lot are non-linearities introduced by overload of a DAC's digital anti-imaging filters. The earlier Audio Precision paper I mentioned describes tests that examine this and concludes:
'Most signals driving into a DAC are not likely to cause any overshoot, and so the amount of headroom beyond 0 dB FS is not relevant to the faithful reproduction of those signals. However, some signals may cause overloads in DACs. The MLS signal is not meant to be a representative signal. It is being used as a (nearly) worst-case signal in order to measure other effects. For example, if—in another device—the kind of signal inversion that occurs in the trace of DAC “A” were to occur only just above full scale (rather than at +5.3 dB FS) it may then produce audible artifacts in the presence of some high-level material.'
page 102.