biggest thing is the 3.8L likes to burn oil. Chrysler says 1quart for every 1,000 miles is normal. To me, thats bad, but I dont make the rules, i just fix them. The biggest thing I have seen on these engines that causes them to burn oil is the cylinders walls get egg shaped. I have found that most engines that have this problem the biggest wear point is close to the bottom the cylinder wall. Not enough to cause a misfire but enough to allow oil to seep past the rings.
Now I have noticed people who switch over to a heavier weight oil burn less oil than if they use the 5w-20. People who run syn. oil burn more oil as well. My advice, summer time, run heavier oil and switch back to 5w-20 in the winter. Change the oil every 3000 miles and ALWAYS check the oil level at 1000 miles. Doing this can save you from a oil starved engine.