I bought a ZD1011 late last year, so I do not have an extended experience with it. But, I will answer your questions based on the time I have had it, I have not had any overheating issues. It is a robust mower. I have never owned a zero turn mower before this one, but from being around other ones, I can tell this mower has a heavy duty construction to it. Routine maintenance is not bad, but not fun. I have not had to change the oil, filters and whatnot yet due to low hours. But, it has to be greased often, which includes the deck spindles and all the drive shaft fittings, of which are several. (Guys here said a good rule of thumb is grease after each tank of fuel.) Some fittings can be a pain to reach, and I am getting my technique refined each time I do it. Over time, I will be able to do it much easier and faster. I have also bought a long grease gun hose and have a lock-n-lube tip on it. I consider the long hose a must for ease of greasing the mower. I could not get the lock-n-lube on a couple of fittings though.
It has a radiator cover and inner screen. That must be cleaned often as it accumulates clippings and whatnot. I would think neglecting this will cause overheating.
With all that being said, I have enjoyed the mower, but I have never had a machine like this. My mower for the last 15 years has been a Husqvarna 48" standard riding mower.. Quality of cut with the Kubota, is OK. I have read the ZD mowers don't cut as well as some of the competition. The ZD1011's front axle can be locked or set to articulate. If set to articulate, the ride is not as good if the ground is not flat with bumps and dips. I think it will cut better set to articulate, but I had to set my axle fixed, but the ride is better.
The biggest "issue" I have had with the mower is that it is heavy. I think it weighs around 1400 lbs. I have an awful clay soil and spring weather kept me from using the ZD1011 this year, and I had to resort to using my old mower until the soil dried out good enough. I have to be careful not to make marks in the yard from sharp turns, and it is compounded when the yard is wet. I realize technique is important, and I am learning to drive it correctly. I have also found I need to be careful of going down a slope, especially when damp. The mower is so heavy, and the momentum will cause the mower to slide rather than stop.
I have had to recently change the dust ejector on the air filter housing after only 25 hours. It simply melted and I think it is common for them to melt after a while.
Overall, I happy with the mower though. I can cut so fast with it compared to my old mower, but that is just the difference between a zero turn and old mower like I was using.