Four general issues that come to mind are hesitation, power steering fluid, timing chain stretch, and fuel economy. There is a sticky at the top wrt hesitation, and suffice to say it can make the car feel lumpy to drive from a standing start. You do get used to it after a while and learn to compensate. The steering fluid issue has been well discussed, and the worst case scenario is that a new steering rack will be required. That said, some of us have the red steering fluid from new and have had no issues with our cars. The timing chain issue has affected some cars with as little as 20K on the clock, whereas others with 80-100K are still on their original chain. Finally, fuel economy is poor but if your mileage is low then spending a little extra on fuel is a small concern. An equivalent diesel will cost more to buy and run, and will be more problematic if you primarily do short journeys. These are only potential concerns, and there is nothing to say they afflict all 159s out there.
We have two young kids, a 159 and Qashqai, and my wife previously owned a 147, so I'll give you my impressions on a 159 as a family vehicle. I think you can manage fine with a 159 as a family car. However interior space, particularly in the back, is a little tight. To be honest, after fitting the car seats, I don't think the back is much more spacious than our old 5-door 147 in terms of legroom, or getting the kids in and out. A travel system will occupy a good portion of the boot, but the size is adequate. It's worth taking your car seat and child on a test drive and checking out the space for yourself. Some taller drivers have found it can be a tight squeeze in the front if there is a car seat fitted in the back.
You will find space tight if you plan weekends away (visiting family etc) where you need to pack a lot of stuff. I suppose most people use their family car for a lot of short trips, and the longer trips are an exception. You can always pack light, but sometimes it is nice to be able to throw a load of things in the car. This is one area where our Qashqai beats a 159 hands down. Dynamically, and looks wise, it is the polar opposite of a 159 though.
FWIW, I think the 159 is a cracking car. For the price, there's nothing close. Mine has done over 100K and there is no hint of a rattle or squeak. The engine loves to be driven, and the car handles well. The looks are still exquisite, nothing in the same sector comes close. Buy on condition and history. The 2.2 petrols tend not to shift quickly, so give yourself time to look around. Lusso spec vehicles are cheaper than Ti spec, but the latter has a host of extras as standard, including folding rear seats. The suggestion of a 5-door 147 is also a good one. But you are looking at regular cambelt changes versus a chain driven engine in the 2.2 JTS. All the best with your search!