I've read where a lot of people are having or have had similar problems with the Neon that I have had. When I first got the car, I noticed that the transmission shifted a little hard from first to second gear. It progressively got worse (hard jerking and lurching), and I figured that is why I got a really good deal on the car.
Finally, the speedometer and fuel gauge stopped working and the car would only operate in second gear. It turned out that it was just a wire that deteriorated on one of my speed sensors on the transmission. I spliced a new wire on, and it has been fine ever since.
I have also noticed slight surges at freeway speeds, which initially worried me. I noticed this first on a 1,600 mile road trip that I did last year to Denver from LA. The cause of this was having the defroster on. When the compressor kicked in for the defroster, it put a slight load on the engine, and the lock-up torque converter would disengage. It is definitely an annoying quirk, but nothing that should pose any problems. Funny though, I haven't noticed this with the air conditioning on, just the defroster.
Lastly for the problems, my engine is a little noisy and rough at idle. It is just a typical Chrysler 4 cylinder engine. It is smooth and fairly quiet at when running down the road.
Overall, I give praise to the car. It has never left me stranded, and I haven't really done the routine maintenance very routinely. Although the interior is made out of plastic, it looks decent and is free of rattles.
I like the way the way the car rides and handles, and the acceleration is good, but not impressive.
Comfort is top notch for a car in this category, for when it was made. It is a small car that feels roomy, and the seats are nice and supportive.
I don't understand why Dodge didn't have cruise control as standard in this model.