Hello from finland, this is my fist post to this forum.
I have 2002 model Trajet, and I am interested, which are this cars typical problems etc.

My Hyundai

 

If it is the same 2.0 litre we get in the Elantra in the U.S., it'sa pretty good engine as long as it's properly maintained. The biggest issue is making sure a new timing belt is put on at 60,000 miles/100,000 km. It has an interference engine, so if that belt breaks it will cause a lot of engine damage. Also, make sure the right oil filter is used. The filters for Honda cars also fit, but they have different specs for the bypass valve and can result in oil starvation to a Hyundai engine. I've head of that engine going up to 300,000 kim or more.

One thing that seems to go and results in the engine running very rough or not running at all, is the Crankshaft Position Sensor. It's fairly easy to change out when it goes, but the part is kind of expensive. Also, sometimes the Throttle Position Sensor fails. I would not worry about either one of those until they happen; sometimes they never fail. But if it seems like the car was just shut off and won't start, it often turns out to be one of the sensors that feeds the fuel system.

 

Oxygen sensors ..... do follow the schduel maintenance as my advice to you....

 

Overall, it's a good choice as a people-mover vehicle. Great in space and comfort for long driving journey.
Setback is only only don't expect it to provide a fast pick-up like a Posche. It's designed for cruising; notF1 racing!
Gasoline consumption is relatively within expectation for a vehicle this sized. Honestly, itsaves fuelfar better than KIA (another Korean-made brand).