Are there any problems associated with the 2002 BMW 318ti?

The engine in the car you’re looking at has the codename N42. It has a timing chain rather than a rubber timing belt, so that should not need to be changed for the life of the car. However, life is not always that simple and the N42 has a bit of a reputation for developing wear in the tensioners that keep the timing chain taut. If that happens, you could have a chain loose enough to jump a few teeth on the timing gears and destroy the engine in the process. So a service record and close inspection of the engine is called for before any purchase.

This model BMW was also caught up in the Takata airbag recall debacle. As a result, many BMWs of this era were actually bought back by BMW and scrapped as the cost of fixing the airbag woes was greater than the value of the cars themselves. Make sure any car like this has had the airbags replaced and is not a candidate to be crushed rather than fixed. Quoting the car’s VIN to a BMW dealership should reveal all.