It's not a random note - it plays the first note of the whole score. You'll also notice that space+click to start playback at any measure, if you happen to click left-most in the measure on a time signature change, it will play back from the beginning. Why? Who knows ...

By the way, if you scrub only one staff (Shift+Ctrl+space+click) it does NOT do this

This is present for a long time in numerous versions. I have reported it to MakeMusic's support, but this has never been fixed.

It is indeed the first note of the piece. It happens on double barlines, too.

Any idea how we might get this sort of perennial problem fixed? I have never posted anything because I assumed that obvious bugs and flaws would be noticed and addressed. This is not the only issue that has persisted through multiple versions. Does MakeMusic reply to these threads? 

MakeMusic almost never replies to these threads, nor do they fix many of the bugs (some existing for years ...). You should nevertheless submit a request (see top of the page), and good luck! If you use this feature a lot and it if really bothers you, you can insert a blank measure of any length at the beginning (start your measure number region on the second measure), and then you will no longer have this problem while scrubbing. When you're finished working on that flle, just delete the first measure again.

Thank you! I'm grateful for the tip and will do as you suggest. Do you happen to know a work-around for the fact that the scrub feature ignores any solos or mutes selected in the score manager? (I am aware of the control+shift single-staff scrub.)

The only way is to zero the instrument volume of the muted staff in the score manger by typing it in - or, quicker perhaps, in the mixer window with the fader. However, depending on how you have set up your instruments or instrument groups in separate banks, you can mute a whole bank with whatever you have assigned to it, it with a fader there, in the VST Banks & Effects window, and you will then not hear it while scrubbing.

Good tips, thanks, Michael, a.o. the added blank measure at the beginning.

Thank you both.

The "parasite" note is not always the very first note (my experience), but a note or chord located somewhere in the first measure, usually a long value (half note, for instance). Even more bizarre !

It's very annoying - especially if you have a piece that goes through several key changes....Scrubbing plays the first note of the first measure of the piece (regardless of its position in the measure).  It also plays over final bars, key changes, double bars and a couple other scenarios... but if you place an empty measure at the beginning of the score the scrubbing issue stops (though it can stutter)

It's very annoying ...

Talk about very annoying the mixer itself needs a total revamp.