We have put two new plows into service in the last two years. In my experience, most problems will come from the installer cheaping out and taking shortcuts.
Regarding the plow as built, check nuts and bolts and test the hydraulics prior to the snow. I had two fitting leaks on the last new ones - poor work by the dealer. Usually a hose will burst when it is new, from a poor crimp, or go a long time before it weakens with age or abbraison. Hoses are cheap, so stock those. I also stock spare solinoids incase one sticks or leaves altogether.
I have never been impressed when it comes to dealers installing wiring. I guess I am a belt-and-suspenders-guy when it comes to this, but wiring will go south at the worst time, and be the hardest thing to find and fix. There is a rule about that somewhere. I have gone to the extend that I have either left instructions on what to do for the installer, or told him I would do some of the work myself or check and redid his work at my shop. Several corrosion problems from poor work taught me to take lots of care here. No trouble since. Get so dielectric grease- wonderful stuff - use lots, its cheap.
A little bit of peace of mind comes from this exercise, and you should have no problems with your new push.
As far as plow problems go, John's pretty much covered all the bases.
For spares to carry, in addition to the hoses & solenoid(s) I also like to have a couple extra fittings on hand that attach the hoses to the power angle cylinders. Not hard to change if one gets broken off - unless you don't have one with you! And of course, if that happens you'll be wanting spare fluid to put back in the system.
Western sells a plow repair kit with a tool box and nice winter cap. It is well worth the cost, it has all the extra pins and clips, along with an extra hose.
We carry 6 hoses, needed 3 of them for one storm alone.
We used to do field repairs, then we did field service. Now we do something different.
Now that I have some 30 + or - snow plows out on the road during a storm, each truck has the 2 things on it. 2 ton come a long, and an excellent radio. 10 trucks have chain saws incase trees fall and block the path.
When a truck breaks down, if the plow won't raise, we use the come a long to raise it, cinch up the chain and go back to the shop. After doing field repairs by truck headlights, dropping tools, parts ect. I have found it is easier to bring the truck into the shop. This way you can work in a warm place and if ya drop something it's on the floor.
However we also have a mechanic/ yard guy at the shop during any storm. So once the truck gets to the shop, it gets fixed fast and correctly. Now you wonder what we do if a loader breaks down, well we either do field repair if it won't move and we can fix it. Or we have a tri axel and trailer ready to go, to go get it.
I wouldn't shy a way from stocking repair parts at all, we have enough spare parts to be a plow dealer. However I would make the repair in a garage or shop if you have one. It goes quicker, is done correctly the first time, and is much easier.