Nakamichi 505 or the Dragon ?

If playback is the only (main) concern, and you have a big budget, the dragon would be an excellent choice. Especially if you don't want to fidget. If you are playing cassettes from a variety of sources, it is inevitable the you will get tapes recorded with a variety of azimuth adjustments, and the dragon will automatically align itself to play them back at their best. You will get far better use of a cassette collection this way. If you have a large collection, it makes that collection that much more valuble.
If you are not recording and not primarily using the dragon for that purpose, the other reliability issue and alignment issue actually becomes less. With alignments one thing leads to another and effects another, and the complexity of the dragon along with its self-aligning nature makes it harder to keep these alignments at the critical best, which is why the zx-9 and others are used for the absolute best recordings. As parts age and wear the need for alignment is still there, and the alignment issues will compound and make recording alignment the hardest, and with the dragon, there is MUCH more to align to get this up to spec, but for playback, the self-aligning playback head of the dragon will compensate for this better as other alignments for recording start to fall out of spec. In other words, the complexity of the dragon that makes it harder to maintain for the best recording is an advantage for playback.
While 3-head naks are thought of as great recorders, they are really great players. The playback head of the 3-head naks are really in my opinion the best. A lot of them, including those refered to above, are better than nearly anything (if not all) for playback, and usually by a wider margain than most consider because most people evaluate them for thier recording ability. (I would be interested in what TWL remembers in this regard compared to the tandberg).
To put a finer point on it, while a lot of 3-head naks will still enjoy an advantage for play back because of its narrow head gap and alignable nature, dragon would excell in this regard. The dragon was really made to be the state of the art player, made for customers who are willing to spend the money on extracting the most from cassette playback. While there is more than can and will go wrong with the dragon, for playback it will have an advantage in the alignment/maintenence issue.
It all depends on what you are willing to spend on cassettes. If they are important enough to you for the extra dough of a dragon, you would be a good home for one.

If I may add one note to Basements last (great) reply, the CR-7A will also allow you to dial in the head for playback, though not quite as "flexible" as the Dragon and it is manual, not automatic.

There were many that agree with Basements assesment on NakTalk, those that had multiple Nak's would use the Dragon for playback and another Nak for recording; this isn't to say the Dragon does not make a nice recordings.

I use a Dragon for playback because, as Basement and others note, it is unsurpassed in this application. With the auto azimuth adjustment, it can even play back tapes better than the 3 head deck they were made on. It will not make the best tapes for use on other decks (none of the great Naks will, to my knowledge, because of the narrow heads); Tandberg or Revox would be better for recording because they have very stable recording head assemblies. I had to send the Dragon back once for a complete rebuild. The recording function later broke. They are very complex.

I purchased a 581 when new and really loved the sound however, I replaced it in 2001 with a CR-7A that I bought off of Ebay. I chose the CR-7 because it was reported to make slightly better recordings that the Dragon with the added benefit of autocalibration. I must say that it is a great machine that easily surpasses the old 581. The CR-7 has a playback azimuth adjustment on the front panel and on the included remote control so, you can tweak from your listening chair.

The Dragon does have auto-reverse and all of the other great features mentioned but, remote control was an option.

BTW, I had my CR-7 tuned by Stephen Sank, in NM, who also installed the factory gear drive modification to the transport. A great resource for information on all the Nackamichi models is: http://www.naks.com/

The bx-300 was the first to depart from the older transport design in an effort to lower manufacturung cost. It is still made to operate the same way and with the same specs, but it uses different parts, and is also sort of a transitional transport to the later cr series. The whole bx series seem to suffer from idler wheel issues, but the transports still seem to work well. The bx-300 was a lower cost 3-head, and still I think offers great value for the 100-200 you can get them for. The electronics seem to sound good too.
The 680 series uses an early transport that some consider the best ever made. There are some that consider the 680 series the best naks, but they are less acknowledged because of the zx series. The 680 series had many models that I can't recall specifically, but some had some features like self adjusting record heads and auto calibration in some parameters. The 680 series was the state of the art at the time. While some of the self-adjusting features were gadgetry more than performance, they do not have an affect on the capability of them. The transport is REALLY excellant as far as operation and working on. The electronics are excellent sounding, and I am thinking that you would have to have one side by side with the zx series to decide which was better. As far as that goes, you really could be splitting hairs. There are many slight design changes in all the years nakamichi made basically the same deck, some better and some cheaper.
Aside from the transport, the electronics are tuned. While most sound the same in the context of a system, I have yet to experience 2 naks that sound exactly alike in the context of making a tape and playing it on another system. Some of this is due to the tuning of the electronics, and some due to the design and voicing. I would generalize them as this- the older 580, 680, 480 series as more revealing, detailed, and anylitacal, and the cr, dr, and later as more weighty, punchy, and lush sounding. These are more forgiving of high frequency loss as well. The zx, lx, and dragon fall in between with much of the best of both extremes, being capable of extreme fidelity while at the same time not as touchy. Also, in the early ones, model #'s ending with a 'z' seem to differ from non 'z's' in that they sound closer to the zx series and dragon, especailly for playback. To some, this may be splitting hairs, but some may really tell the difference. When you consider the tuning aspects on sound quality, as well as the context you would use the deck, some might consider the bx-300 close to the dragon. My personal favorites are the 580 and 680 series, tuned PERFECTLY, as I feel I can get just a little more from them than the zx series. (I am currently using a 582 as my main recorder, because my favorite 582z is out of tune!)
Hope this helps and is interesting.
I don't know what the mfsl geo tape is, but if it is an azimuth alignment tape, or has an azimuth alignment recording on it, it would be excellent. I use a nak azimuth tape which has a -20 db 15khz tone recorded on it to get the play head in close alignment. I then record a 15khz like I am adjusting for bias using the built in test tones on the deck. I then flip the tape over and record the same without readjusting anything. If it is within 2 db on the meter, and hopefully one, and not dancing around more than one db, that is good. If anything changes in the alignment, the first to go will be the azimuth, and the meters will fluctuate as the tape goes out of the critical range, and looks like flutter. There are variations in tape shells, so flipping it over doubles any variation. I can get more into it if you like, but I have been long winded enough, time to post.