My Garmin GPS swivels when answering a cell phone call

Sounds like the ball joint has loosened. You may want to remove the cradle from the ball joint and clean both the ball and socket with alcohol. If this does not help, try to tighten up the pivot area by putting a small, one layer piece of paper towel around the ball before connecting the two together. It will take up some of the slack in the joint as well as creating some friction to hold the two more solidly. Start with just one spacer since if you add too much, you may break the plastic grip fingers within the socket. To hide this paper towel spacer (since it will likely be white in color), get a black permanent marker and "paint" the paper towel spacer black with the marker before installation. The excess/overhanging paper towel spacer can simply be torn off from around the ball/socket joint.

Another issue may be the touch screen sensitivity...do you have to press it hard to register touch presses? I've seen units with absolutely horrendous touch screen sensitivity that required such hard screen presses that the unit would in fact move the entire unit at the ball & socket pivot joint, despite that pivot joint being tight.

Yes, this brand new Garmin GPS screen is not sensitive at all. I need to apply much finger pressure in order to push the ANSWER button down at least 2 times and it's like a meteor crashing into the Moon as you can see the ripple effect on the screen.

You should really consider exchanging the unit since it is brand new. If possible, try the new unit's touch screen in the store to make sure it's working to your liking before leaving the store. The touch screen should not be that difficult to push to register a screen press on the unit and you should not have to live with a bad touch screen.

You didn't say which holder you are using but if you are using the bean bag there is a lock on the swivel so it won't turn when you press on the screen. I had the same problem a couple of times good luck.

If your unit is a 7x5T try running Webupdate the new models had a screen sensetivity issue but it was fixed on the 1st update

On the 680, I could adjust the touch screen sensitivity.
Have not had the 760 long enough to see if it does that. I think all units should have that option.

On the 7x0 & 7x5 units (along with all other nuvis), you can calibrate the touch screen but you cannot adjust the touch sensitivity. All nuvis have the ability to calibrate (where the touch presses register) but not to adjust the sensitivity. I've owned a nuvi 350 since it's release and it never had any ability to adjust sensitivity. The calibration and sensitivity are not the same.

Thanks to all of you. Your comments and advice are invaluable!

Sadly, my brand new Garmin 265WT's screen feels very spongy. I am returning it for another brand new unit.

From your subject, I thought you'd found some new feature. How cool would it be if it would automatically swivel toward you when you got a call!