After taking my 244 this morning to Jiffy Lube to get the oil changed, I noticed that the car sounds a little louder than normal when accelerating hard in first and second gear, above 3500 or 4000 rpm. Also, a couple of times while I was driving it this afternoon, I noticed as I accelerated that there was a lot more vibration of the floorboards than normal.

I'm guessing the problem probably lies within the exhaust system. We've had the most problems with that, having to get something fairly major replaced every six months or so, it seems. By now it seems like we've replaced the entire system and that there shouldn't be any problems, but I think that there may be a hole in a pipe somewhere. Any guesses?

MAC_MUZ has a good point. Aside fromn the mounts causing the Jiffy guys to push the pipes around, I would check where each pipe exits and enters the two mufflers. Many aftermarket mufflers are just not welded very well and the pipes spin and come loose where the go into the muffler.
--
'75 Jeep CJ5 345Hp ChevyPwr and two motorcycles: it wasn't Volvos safety , it was Longevity that sold me

Might be dead engine mounts and the oil change guys had to push up the engine to get the filter out, and they by doing so violated a bad exhaust....

The rubber mounts hate oil, and so drop dead... I know of no way to not give a great dose of oil to the mounts at each filter change unless you cover them with a baggie, and no one does... That would be my guess... Mac