I have just upgraded my Dell XPS L322X laptop from 16.04 to 18.04, and the behavior of my trackpad changed. Previously, I could drag to select text or move objects by clicking the left button of the pad and moving my finger. Now, I can only do so by tapping twice and moving. I do not know if tap-and-drag was working before.
I have looked at some configuration options available at xinput and at the Synaptics driver, but none of them seem to be related. In particular, disabling tap-and-drag does not make click-and-drag work.
This question reports a similar issue on 17.10: 17.10 upgrade: Drag & drop on touchpad doesn't work.
There is a possibly related bug report on Launchpad: https://bugs.launchpad.net/ubuntu/+source/unity-greeter/+bug/1763209?comments=all.