Guys mention the lack of parts for the 624, never worked on one, but I'll take their word for it.
Used Tractors For Sale at TractorHouse.com: John Deere Tractors, used farm tractors and farm equipment, tractors for sale, Case IH, New Holland, Agco, Kubota only showed one tractor under 7K in NB, and that was a compact with a loader.
Found a couple on autotrader of all places:
Massey 165 industrial with the world's ugliest half cab, comes with tire chains:
Used 1969 MASSEY-FERGUSON Industial 165 for Sale In FREDERICTON, NB - 4544803 - autoTRADER.ca
IH 434, a little smaller than the 624 you're looking at, but a Doncaster (England) built tractor, and parts are easier to get. Loader and tire chains, and a snow blower:
Used 1971 International Harvester 434 for Sale In FREDERICTON, NB - 5204566 - autoTRADER.ca I'd give this one a look if I were you.
Most common stuff to look at on most any tractor is - oil leaks, small ones are no big deal, but replacing hoses gets expensive. Motor starts/runs without excessive smoke. Older diesels will commonly have a bit of bluish smoke till they warm up, and a pump that's twisted up a bit will smoke black under load, but white smoke (head gasket) or blue smoke after warmup (rings, etc) can mean engine work soon.
Clutch should engage and disengage smoothly, and not slip. Brakes should be in good working order (both sides - most tractors have a brake pedal for each rear wheel to help with turning). A brake job on a tractor can be expensive, as many of them are inside the axle housing and take a lot of work to get to.
3 point hitch, hydraulics and PTO - the 3 pt should lift what it's rated for or close to it, and hold it up while running/moving around. Many older tractors the 3pt will settle - sometimes quickly, after the motor is off. ALWAYS lower 3pt equipment before getting off the tractor, running or not! Hydraulics should lift smoothly - a lot of chatter means low oil or a problem with the oil pickup, weak or no lift means hyd pump is shot and could be a spendy fix (some are inside the transmission/rearend). PTO should start up fairly smoothly and not slip, if the tractor you're buying is at a dealer, ask em if they have a dyno and if it's been on it. Most shop dynos are PTO, and any problems will show up quickly at full load. PTO should stop when turned off. Many older tractors, it's common for the PTO brake to not work anymore, it can take a long time for something with a lot of rotating mass to slow down, but it should come to a complete stop.
Wheels and tires were mentioned above, but I'll say it again: Tractor tires ain't cheap! Worn out rear tires will go a long time for occasional use, and with chains will go about anywhere. Bad weatherchecking can mean a failure soon, regardless of tread. If tires (usually rear only) are filled with fluid for more weight, watch for rusted rims, especially around the valve stems. I've patched em before, but it's a lot of work (tire needs to come off), and it depends on finding some good metal left on the rim to weld to, as well as a little fabrication knowhow.
Loader and bucket: Buckets get dinged up and patched up, but if it's real twisted, it's gonna suck to work with. New buckets aren't real cheap, but they are an option. Loader arms take a beating, and it's not uncommon to see repair welds on em. A good job, preferably with a reinforcment plate used, isn't a big deal, but a lot of cracks that haven't been fixed, or caveman looking fixes should be avoided. Look closely at all the pivot points for excessive wear, cracking, etc. Like mentioned above, buckets can settle, sometimes faster than you'd think. Keep em on the ground if you're not at the wheel. Oh - and PLEASE don't drive around with the dang thing way up in the air! Keep it within a couple feet of the ground unless you need to go higher, and you're a lot less likely to roll the tractor over.
Yup, I've written another tractor book. I probably still missed something, and someone's sure to correct me on something, but it gives ya a few points to ponder.