I've had an n53 530i for the past 4 years and 55k miles (now at 125k). As already said, High Pressure Fuel Pumps, injectors, coil packs are all potential weak spots and can be fairly costly, but I've had no issues with any of these on mine and don't think any were attended to by the one previous owner. These can use a little oil. Mine is using a litre every 2200 miles or so but seems to be fairly consistent at that, except when there's a leak, and they can be regular enough. This has been an issue on pretty much any and all BMW engines since the m52 or so, so not n53 specific. I've replaced the rocker cover gasket and have one currently that I haven't figured out the source of just yet. The rocker is easy to identify as it often drops some oil on to the exhaust manifold so you'll smell it as it burns off. I've replaced the crank breather valve on mine too.
Most of the issues I've dealt with on this car aren't n53 specific and I can't say whether I've just been lucky with the bigger ticket items on mine but so far so good. Most of the issues I mentioned you'll likely have encountereed on the n52 if you had that for any length. The power and torque of the 330i engine makes for a very easy drive, notably so even compared to the n52 I have in the 630i. Having said that, the n52 is definitely a more interesting aural experience. The n53 is very smooth but not as tuneful.