Dun, I think BigBull hit most of the highlights. I have/had an 851 which I think is pretty close. The 851 has wear strips that the floor chains run on, kinda sacrificial because they keep the floor chains from eating up the floor of the baler. Anyway, those need to be replaced from time-to-time. Floor chain bearings are a must. As you know if one of them go out you will have a nice fire to roast your marshmellows on. Also, BB mentioned the bars. On the 851 the bars run on a rubber tire sort of thing in the middle front kinda low (just above the pickup reel). That "tire" needs to change when it gets worn. Otherwise the bars will be slapping bare metal and will break the bars. Then you got a mess. Don't be standing anywhere close to it if a bar breaks and you can't get to the PTO quickly. There's a couple of cables running over the top of a cam at the top of the baler that is connected to the bale tensioning springs. Make sure they are in good shape. Lets see, what else. You can choke one of those old balers pretty easy. Then you have several minutes digging the hay out of the pickup. Oh, yeah. once you get a bale formed in the chamber don't stop and try to restart the baling operation. You'll be replacing the shear pins in the drive line. Might be a good idea to stop by your NH dealer and pick up a package or two of the bolts (shear pins) because there isn't anything else that will work. They are metric and a 1/4" bolt won't fit and a #12 bolt is too small and will break first time you turn it on. Throw a couple of 10 mm wrenches in your tool box too.
Someone mentioned tensioning the floor chains. They are spring loaded and you can increase (decrease) tension by adjusting the 3/8 bolt that runs through the spring. This is done from underneath the baler. You will have to run the baler up on a pile of dirt or something so you can get to them. Service manuals are available. There's a couple of places to get them. You can get them through NH but I don't think they publish them anymore. Everything is "outsourced" these days and be prepared for sticker shock. I had to pay over $400 for a set of manuals for my new NH. If you don't have a chain breaker you can grind the rivet head off and drive out the link pin with a punch. The new master links come with a clip that holds everything together. If you grind be careful not to camp out on the side plate with the grinder.