<p>Is it correct to say that typically user_dump_dest is on a local drive?</p>

<p>If so, are there issues with mounting a NAS volume to both Unix and Windows and pointing user_dump_dest at that?</p>

<p>If so, what are they? </p>

<p>Are any issues worth not doing this in prod? </p>

Yes, typically (and by default), user_dump_dest is on a local drive.  I wouldn't expect there are any specific issues with putting it on NAS; but it would have all the potential issues that any application might:  (1) If the NAS could not be reached, Oracle would not be able to write out user dump files, and (2) the write latency would be increased.  The latency issue is probably only important if you're doing large-scale tracing to diagnose performance issues, as the write latency would impact the timing measurements.  I would expect that if the NAS because unreachable and Oracle tried to write to it, it would silently fail.
I don't think I would do it unless space constraints on the local disk forced me to.  But generally the contents of this directory should be insignificant relative to your data.