I don't personally own a Dodge Avenger, but my best friend purchased one around 1.5 years ago, and I have ridden in it as much as my own car.
The Avenger is a nice, sporty looking car on the outside, but on the inside I found it to be very cramped. This is NOT a car you want to haul more than 2 people around in and it is uncomfortable for car rides over a couple of hours. Also, it may seem petty, but the cupholder and storage situation, as well as the trunk space, are not anything to brag about. You cannot fit more than 2 medium suitcases in the Avenger's trunks comfortably, and there is only 1 good cupholder in the front of the car...not cool if there are 2 people with Sodas!
The gas mileage is not as good as the dealer indicated it should be. It runs 2 to 3 MPG less than the dealer said it would, which adds up over time, especially when gas prices are creeping up.
The one mechanical problem that my friend has had with the car related to the odometer. The odometer was running faster than it should, resulting in around 4% more miles being put on that were actually driven. It was fairly simple to fix the problem, but still an annoyance.
If you are looking for a sporty second car, or you are a single person with very little need for long trips and a lot of trunk space, the Avenger may be a good car for you, but otherwise I don't think I would suggest it as a car to buy.