there could be a couple rubber pucks the size of a $2 stack of quarters that press into the underside of the car in between the resonator/muffler that may be missing (not an expert on this model)
not sure if the same on the 240, but on 300 the down pipe is secured via a u-bolt attached to an arm bolted to transmission that has rubber isolators that could not be doing their job anymore.
likewise, the driveshaft center bearing is surrounded by a rubber donut where it is attached to the car. you don't want that to fail completely while driving. ask me how i know
this would be a great time to inspect the flex-disks, or guibos, if you prefer.