It's hard to sort your questions out from your message. You might do better, for example, posting a message that says "Can you please post your empty weight and momoment for your airplane, along with the year model?" I think folks would answer a specific question like that more readily.
You asked about quirks with the various models, and that is a really hard question to answer in a single message. The Cessna Pilots Association has a list of the differences between models, and it runs several 8 1/2 by 11 pages. You get this info when you attend their systems and procedures course, but if you join their organization, I suspect they would send it to you. Here is a capsule of *some* of the major differences, done quickly from memory.
* The 336 was produced one year, has 195HP continuous engines, fixed gear, and a very different rear engine cooling system than all other models (single large cowl flap on top of the engine, rather than a fixed scoop)
* From the '65 337 to the '72, there are a number of gross weight increases. All of these airplanes have main and aux tanks (I suppose someone may have ordered one without the aux, but I have never seen one like that). There are normally aspirated models, and starting in (I think) about '67 there are turbo models available.
* In 73, the turbo model was temporarily dropped, replaced by the pressurized model. There were also normally aspirated available. Both are based on the same, newer body style, with an airstair door rather than the standard Cessna door used previously. They have main tanks only, but the capacity is the same as the previous main/aux combination, about 123 gals usable, so fuel management is simpler. The gear was changed from engine driven hydraulic to electrohydraulic at this year.
* In 75 the larger, 146 gal tanks because available. In 76, the back seat was changed to one that slides from the rear to the front of the cabin rather than being in a fixed position. Turbo (but not pressurized) models came back somewhere in here, my memory says '78, but I am not sure.
As for things to look for, other than getting a well maintained one (see other messages on this subject on this site), today are there are suprisingly few things to pay close attention to. To again hit the high points (meaning you need to research all of this more closely, as I am omitting important details):
* There are a very few airplanes around that are still on their first engine runs (TT and engine time less than 1500 hours) which have light case engines. You should check the engines on these airplanes VERY carefully for case cracks, and plan on an overhaul soon.
* Except for the 336 (I think), all 337 models require a spar inspection at 5000 hours, and every X hours after that, except for pressurized airplanes where the inspection begins at 10,000 hours instead. You can read more about this test in other messages on this site. If the airplane has been used for pipeline patrol or similar low level use, the test is due earlier, 3000 hours if I recall correctly. I would have an airplane that has had this use tested before buying it, regardless of hours, if it were up to me.
* Control cables are becoming an area for examination and proactive replacement, see other messages for more.
* The Cessna autopilots, while a great piece of equipment, are becoming increasingly hard to maintain. It is a significant plus if an Stec or other autopilot has been installed in the airplane.
Other than that, it is all the usual stuff for any airplane you might buy: get the AD's and paperwork checked, and I can't emphasize enough (in my opinion), *don't buy a "fixer upper"* unless you have access to free maintenance labor. You'll never recover the money it takes to get the airplane up to snuff. And there are lots of "fixer uppers" around, because the airplane is cheap relative to other twins, and folks with limited budgets buy them, then are unable to pay the normal costs of owning a twin, so they defer a lot of maintenance, which you get to pay for after you buy it.
That's the stuff that comes off the top of my head. I am sure I got some of it wrong, and others will correct me. Ask some more specific questions, and many folks here will be glad to offer opinions and assistance from their experience.
Kevin
webmaster@337skymaster.com