After reading most of this thread, I am intrigued and excited about all of the music listed. I see much I love; Rush's material as well as Van Halen's 1984, some newer stuff such as Aloe Blacc, Adele, and Florence + the Machine, and a few electronic/ambient artists such as Boards of Canada, Shpongle, The Orb, and The Flashbulb. I know plenty of other stuff here, but it should be fun discovering other people's interests in music I haven't heard. And this brings me to my next point...
Obviously much of the music produced in everyone's choices are most likely (but not certainly) a look into the types of music they spend some of their time hearing. So most everyone's picks are based on everything they've heard, and nobody has heard it all. This makes me think that there could quite possibly be a flawless album for each particular genre of music (due to shifting interests in genres between head-fi members - everybody that listens to music for that matter). It is also interesting to note the differences between favorites and flawless albums. LugBug1 has brought this point into the conversation. I believe a 'flawless' or perfect thing is free of flaws or imperfections. Perfection, by dictionary definition, is hard to achieve and I don't want to say it is impossible, but I don't think there should be so many 'perfect' things (in this case albums in the same genre of each person's list) because if everything is perfect then they lose their exclusivity of perfection. As such, I believe there should be a flawless album for each genre. IMHO, the flawless album in 'whatever genre' is the epitome or quintessential 'whatever genre' album to have. Of course this is still subjective because it is based on what the listener has heard and picked as the best one, but every other album in 'whatever genre' should strive to be as good as the best.
I suppose though, following the criteria of being a good play front to back with no fillers, there could be many different albums people enjoy that fit the bill. Regardless of what I mentioned above, everyone is entitled to their own opinion! And the more music the merrier!
So my contribution to the ongoing list: in the electronic, more specifically ambient (a little abstract too), genre, I think of Boards of Canada's (BoC) Geogaddi as the flawless album. Although I love BoC's debut Music Has the Right to Children [MHTRTC] (mentioned earlier in this thread), I believe their sophomore full length release is deeper and more meaningful than their first (not as heavy on the D&B, more ambiance). The album is classic BoC, filled with liquid melodies and the warm, lush, analog sounds of the 70s and 80s (or so I've been told, I wasn't around then). It inspires nostalgia (I find myself daydreaming about childhood). As happy and innocent as some of the album sounds, it is equally balanced with dark and menacing (even scary) themes. BoC also placed backwards samples in the music; playing it backwards allows one to find these 'Easter eggs' or hidden gems and yields a different way to listen to the songs (almost new songs themselves). IMO it is just as engaging as a forwards play through. The promo vinyl release for Alpha and Omega (one of the songs featured on Geogaddi) can be heard at two different speeds for two different sounding but very enjoyable songs: the original at 45 rpm and a mellowed out 33 1/3 rpm version. The track selection fits together like a puzzle, and is meant to be listened to as a whole. In an interview with Marcus and Mike, the Scottish duo that make up BoC, there is discussion of the music created for Geogaddi. Over 90 songs and many samples were gathered, but... Only 22 (23 if you count the silent Magic Window) were picked for the actual album (see link below for more information). Striving for perfection, anyone?
"Play Twice Before Listening" by Koen Poolman
http://fredd-e.narfum.org/formerboc/interviews/#oor
An interesting read. Perfection is discussed in regards to music (specifically BoC and their releases) throughout the whole page.
Thanks to anyone who reads this all. Hopefully you try out Geogaddi and enjoy it. Might not be for everyone, but an album that can be played forwards or backwards, slow or fast, and as a whole instead of individual songs is a flawless masterpiece to me.