Another easy to way fix either of these issues with PlayDelayed or PlayScheduled is to wrap them in an Invoked Method instead.

still in 5.1.1p1

Observed here, very frequently but inconsistently in 4.5.3f3 when calling PlayScheduled from a coroutine.

Skelly, thanks for the workaround suggestion - much appreciated.

I found a workaround at least for playscheduled. Right after you call playscheduled, call SetScheduledStartTime with the exact same value. Seems to fix this issue.

btw its not related to the start function. PlayScheduled has a bug in it no matter where it is called.

I also see this in unity5.0.0f4. its true in editor and on ios- exact same behavior. some tiny part of the sample doesnt play scheduled into the future, it plays immediately, and then the rest of the sample is playing at the scheduled time. I can provide a simple project that shows this effect very explictly.

Unity 4.6.2p2

Getting this issue when calling from ui button events

I'm getting this issue too, but I'm calling it from a function that is triggered by a timed SendMessage from another script, so it's not just limited to the Start() function.

When called from the Start() function, PlayDelayed() and PlayScheduled() will play a short (1-frame?) segment of the audio clip immediately, then pause. At the scheduled time, playback will then resume from the point where the clip paused.
This creates unpleasant sound "glitches" and timing issues with stitching audio tracks together.
This behaviour does not seem to occur when the functions are called from the Update() function.