If you can, can you tell me what I should be looking for before the warranty is up (I think it's 5 years on the powertrain and that will be in 9/08). And also, did you get this info by working for a Hyundai dealership or from other's who did? Not doubting you, just curious since you have a LOT of info.
watch out for components of the 4WD system, which are inherently weak in the santa fe (weak in terms of prone to failure). this includes the transfer case and the rear differential.
if any of these components fail within the bumper to bumper (B2B) 5/60 warranty, then they will usually not put up a fight, but they will want proof of maintenance as specificed in the owner's manual.
the sticky part comes in with the extended 10/100 powertrain warranty. as specified in the warranty manual, those parts do count as "powertrain" components and are covered under the extended warranty. and most of the failures are happening at some mileage over 60k, after the B2B warranty has expired. apparently the regional service reps are pressuring the dealers to not cover those repairs after the B2B warranty is expired, either by denying that the defect is part of the powertrain coverage, or by claiming that you didn't keep up with required maintenance (hyundai is VERY picky about that), etc, etc...
i never worked for hyundai, but i owned a hyundai elantra and was a global forum moderator at elantraclub.com. one of the members of that forum (and personal friend of mine whom i've met several times) was a guy who worked at a hyundai dealership, and he brought this up during a forum discussion about warranty claims. he said that they will basically try to weazel their way out of honoring the warranty and that it can require a pretty good fight to get them to "do the right thing". in addition to the santa fe problems, the hyundai accent also had a common problem with an engine knocking noise caused by loosed main bearings. this happened to his brother's accent and the case got escalated all the way to the top of the chain, and they never fixed it. he ended up selling his car at a loss and buying something else.
i'm not trying to scare you into getting rid of your santa fe. but be very diligent about the scheduled service intervals, and if you do need major repairs and the vehicle is still technically under warranty, don't let the dealer try to weazel out of honoring it.
if you bought your santa fe used, this may be largely moot, since the extended 10/00 powertrain warranty does not transfer to second owners.
ETA: oh, and another main point of all this was that much of the warranty shenanigans varies from region to region, as the regional warranty reps have pretty much complete power over authorizing the local dealers to perform warranty repairs. if you have a good regional rep, you may not ever have problems. but if you have a bad one, it can make being a hyundai owner difficult.
i also had firsthand experience with hyundai trying to deny warranty claims on my elantra, albiet using a different tact. they would always tell me that the problem "is not a problem, it is within spec"). so when one of my four power windows started going very slooooooow up or down, i was told "that's normal, we're not going to fix that under warranty... it still works, right?" after two years of this type of attitude, i unloaded my hyundai for something else.