Bodywork corrosion - front and rear offside wheel arches are both suffering, with extensive corrosion on one of the front wings. Apparently this entire panel can be replaced fairly easily though.
Underbody corrosion - exhaust and heat shield mountings have had issues (I ended up just removing the heat shield entirely to stop it from dropping onto the road). Brake pipes also corroded badly. Finally the front crossmember below the radiator has just failed due to corrosion, dropping the radiator onto the road. This is the final straw that will see this car consigned to the scrap heap.
Power steering problems. Had to replace the power steering pump (DIY job with a reconditioned unit) and also had a fluid leak from elsewhere in the system. Some of this could be down to lack of maintenance in an older car however... I'd suggest making sure the power steering fluid is replaced on occasion to help prevent issues.
Issues with brake caliper seals leaking (on two separate occasions, first time front, and then rear a year later).
Developed a small oil leak from a hole in the bottom of the sump, presumably due to corrosion. I fixed this using JB Weld, and have not had problems since.
Central locking is unpredictable. All doors lock and unlock remotely, but will only work with a key if the car is unlocked from the passenger side, not the driver's side. It occasionally locks and unlocks itself while the car is driving.
Leaking from top of driver's door surround in heavy rain. More or less fixed with liberal application of silicon sealant.
Thermostat failed, but this was a relatively cheap and easy DIY replacement.
Windscreen wiper wash control failed, but a replacement stalk from eBay sorted that.
Heated front windscreen only seemed to work on a narrow vertical strip on the passenger's side.
In my time owning the car, front suspension drop links and one wheel bearing also needed replacement.
Usual consumables like brakes, tyres and exhausts, though the full exhaust system, including catalytic converter, came at an eye watering price for such a "cheap" old car.
Quite a list of issues, though most of them could be expected in this age of car, or were relatively minor annoyances rather than big issues.
My biggest issue with it was corrosion related.
The car handled terribly when I first got it - the mk3 diesel Astra I had previously was a better drive, and I had a few "moments" when pushing the car on tight bends in the wet. I really wondered what all the rave reviews had been going on about until I fitted a new set of tyres all round. This completely transformed the feel of the car, and suddenly I got it. The old tyres had plenty of tread, but were just rubbish.
Fuel consumption was generally around 35 MPG, though that is taking it pretty easy - I ride my motorbike if I want to go fast. Long drives would see this rise a bit, and I generally got between 350 to 400 miles from a tank (more often towards the lower end of that).
Plenty of room in the car, and we found it comfortable for long trips. I took it from Scotland to France and back once with no problems.