Welcome to the forum. Without knowing your needs/desires for the tractor, it's hard to give much advice. From what I've seen, the MT372D is a US market 12 pto hp, 15 engine hp tractor, roughly comparable to my Yanmar 1401D, though a bit smaller.
I don't know how new you are to any other sort of equipment, so a quick explanation: Don't compare the 15 hp of these tractors to the 20 or 24 hp "garden tractors" at Home Depot/Lowe's/Sears. That little Mitsubishi, though only rated at approximately half the power, will literally rip the guts out of a garden tractor if you chained them together. If the size of tractor fits your needs, then the machine will work for you, and do vastly more than a 20hp garden tractor with a back blade and/or Johnny bucket could ever hope to do.
One thing that you may consider is that it is fairly difficult to get rebuild parts for that model, apparently. That doesn't mean they aren't available, or that you shouldn't get the machine. Napa should have most or all of the filters and basic service products, for instance. If you are a very casual, low time user, you'll likely never need any hard parts. These tractors should last several thousand hours, or more. If it really does have under 600 hours, and you're only going to use it a couple hours a month, 25 hours a year, you could run the thing 40 years and not have any concerns or issues whatsoever with wearing the machine out.
The danger with these small machines is abuse and neglect. The fact that the axle is "a little wet" in the middle could be no big deal, or a sign of a serious problem. If it has had a loader on it since new, and was used hard, or, worse, in a rental fleet, it may have front end damage. If it's a bit oil damp because the crankcase vents there, it's no big deal. If it's been abused, though, the scarcity of parts becomes an issue. If it's been used gently, it won't matter, because you can use it for a long time and not ever do anything except service it. Look for cracks, wearing, or other signs of abuse where the axle has joints and where the pivot is. Most of these tractors have spindles which make the tops of the tires point outward, kind of like the rear ends of old VW Beetles. This is normal; but make sure both have the same angle.
Who is offering you the tractor? Do you, or they, know it's history? What do you want it for, and to do? A little tractor like this will do almost everything a big one does (the only real exception is lifting capacity and dragging ability scales up or down to the tractor), just a bit slower. Sometimes a smaller tractor can do things a large one cannot, like fit through a gate or between narrow places. If you have a 2 mile long driveway that you want to clear of snow each morning, this isn't the right choice!:laughing: It will take you an hour or more to drive to the end of the driveway and back.
If the machine is in otherwise good condition, though, $4500 seems reasonable but a bit high. I'd say it needs to be a nicely kept tractor for the price, mostly since parts are hard to find. Your location will determine some of the pricing issues, though, as well as the time of the year. Another consideration would be to rent something. If you only need it for a specific job, or very rare usage, it will be cheaper to rent. I've found my loader to be so useful that I wonder how I got along without it; yet somehow I did.
Where is the tractor relative to you, and are there any pictures available of this machine? What are other similar machines (even if not Mitsubishi) going for around there? Hopefully a more Mitsubishi oriented member can give you more specific advice, but the general points to look for are the same. Good luck!
