I ran the stereo analog outs of my BDP-83 to my PC's soundcard and recorded several SACD track transitions. I have a regular BDP-83 running the latest official firmware. The mp3 file can be dowloaded from the following page:
http://mysite.verizon.net/vzepit1s/
I tried to get a good mix of record labels. I literally grabbed different discs off the shelf and every one exhibited the problem. Hopefully, there's something in this list AVSers also own and can try on their setups. I didn't alter the recording in any way...just concatenated all the WAV files together. Don't pay attention to the clicks/pops that are present at the extreme beginning or end of each portion...that's just SoundForge being dumb as a result of my cutting and pasting the 10 small WAVs together.

The single vinyl-like click/pop sound can be heard at the following time indices within the mp3:
01) 00:06; Track 1 -> 2; Jarvi/Dvorak Sym 9 (Telarc SACD-60616)
02) 00:16; Track 5 -> 6; Depeche Mode Music for the Masses
03) 00:28; Track 7 -> 8; Karajan/Mozart Requiem (Deutsche Gramm)
04) 00:41; Track 1 -> 2; Pizzaro/Beethoven Piano Sonatas (Linn Records)
05) 01:00; Track 1 -> 2; Beautiful Mind soundtrack
06) 01:11; Track 3 -> 4; Nutcracker Selections (Telarc SACD-60674)
07) 01:28; Track 3 -> 4; Scarlatti Giardino Di Rose (DECCA 470-650-2)
08) 01:38; Track 4 -> 5; Sarah Brightman Time to Say Goodbye (Angel Records)
09) 01:52; Track 5 -> 6; Mozart Requiem/Kuijken Quartet (Challenge Classics 72121)
10) 02:06; Track 6 -> 7; Gloria Estefan Greatest Hits (Epic 86729)
#6 is the loudest of all, I think.
As a small aside, if I push the skip forward or skip backward track buttons on the remote, there is no pop sound.
Now, I will be the first to admit these clicks/pops aren't huge...but they are loud enough to be noticeable and distracting. What do you think?
If you'd rather not clutter the thread with your responses, you can PM me.

Thanks everyone for taking some time and helping me with this,
Chris