My wife has a 2001 XC70, and a strange issue has started over the past few months, that is happening about 50% of the time.

All the doors will lock and unlock with remotes...but not all of the time. Sometimes, only the driver's door will unlock, sometimes the drivers door and one of the rear doors will unlock with remote, and other times it works just fine.

When this happens, my wife has noticed that the gas gauge will not come out of the "red" / empty area and the "miles to empty" display, does not show the miles.

Once the she stops again, and it seems to fix itself, everything works just fine.

After reading a lot of items on here for other models, I figured it was a ground wire, or pinched wire between the door and body. But have found nothing.

 

The remote should open only the driver door unless you push it twice. Also, in the cars of the late 90's, the latches go bad and don't work when it's to hot outside.

As for the gauge, my guess would be you have an ignition going out or a bad sending unit (maybe a ground near the back where the wires go into the gas tank).