I bought a 2011 Jeep Grand Cherokee with 165K miles on it from a dealer to be picked up next week. The transmission makes a thump when shifting into reverse and sometimes when shifting into drive. The dealer said they tightened a mount that would correct it. Is that what is wrong with transmission or would that thump develop into something serious down the road?
I plan on driving to Biloxi and to Orlando and back to Houston. Is there a mechanic you can suggest in the Houston area to inspect the Jeep to see if it has any engine/mechanical/electrical issues?
dealer said they tightened a mount that would correct it
Only

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If that thing is RWD, it could be a worn U-joint on the drive shaft. They can cause a thump/ clunking noise when you change to R or D. But, if that were the case, you would've felt some kind of vibration when driving down the road.
Transmission and engine mounts can do this when they're worn out. You can't really tighten them to fix "being loose", they need to be replaced. The rubber is deteriorating, leading to looseness.
Thumping can can be something internal to the transmission as well. My '99 Ranger's transmission was rebuilt and the shop didn't do something right, it thuds sometimes going into and out of 1st gear.
Take it to a good mechanic.