1) sounds like your transmission is either low on ATF or has the incorrect ATF in it (or the transmission is on it's way out)
2) sounds like one or more of your motor/transmission mounts is either toast, or it was replaced with a cheap aftermarket mount

 

Did you test drive it before buying it?

 

Always a pause with these cars when changing from Park, not instantaneous.
As stated previously, check mounts. Can put car in Drive w/foot on brake and just hit the accelerator pedal slightly and see if any abnormal movement, try both Drive and Reverse.

 

1. its normal for a long pause/ delay when you shifting from park to drive (Honda stated 2-5 secs is consider normal)

2. This sound like a motor mounts issue (very common on TL), if you do replace the mount please go OEM.

 

The vibrations are probably motor mounts i replaced mine and problem was solved if you notice a hard thump when you give it a good amount of throttle and let off then it is definitely mounts you can also put the car in gear and hold the brake and slightly press the gas if the motor moves then thats your guaranteed sign

 

also oe mounts are very expensive acyra dealer told me 700 for all 5

 

Thanks for all of your responses. Yes of course I test drive it before I bought it.
As far as the mounts go I have some maintenance records for the car and it looks like motor mount was replaced or motor mounts. Not sure. I feel better knowing about the pause in the reverse or drive from park. The owner sad that Acura said that it was normal. I’ve never owned an Acura before so...

 

Sounds like the pre-inspection was not comprehensive!

The delay according to dealers can take up to 3 seconds with our car and be considered "normal". New fluid and a change of the trans filter should greatly improve it. Fluid should be a bright pink red, darker means it needs to be changed. I highly recommend Acura DW-1 trans fluid! You can buy online or from your local honda or acura dealer. (same product, just relabeled for acura).

Vibrations can be due a bad upper trans mount or engine mounts in general. If you notice it more with the A/C on, it's probably the side mount. If A/C doesn't impact it more than likely a bad front mount. Once the front goes it's only time before the rear goes since it's doing more work.

Vibrations when driving the road can occur due to flat-spotting (tires get cold and develop a flat spot when parked). Tire needs to warm up before the rubber can flex and it can come out and be round and smooth. Another issue could be a bad tire balance. If the weights come off or the tire is wearing and causing the tire/wheel combo to be off balance, you'll feel it. Discount tire is the best since they have the HUNTER balancing machines that help the TL ride smooth. It's sensitive to where as little as 1/2 oz can make a large impact on what you feel!