I noticed this question is posted frequently without solutions being given. The problem makes the touchpad difficult to use, it is a serious problem.
In the end I found a solution (for a Dell XPS 15). It is all about the setting for FingerPress. When not set explicitly, the value is 256, which is way too high (value can be checked by typing "synclient -l". You can set it to a more reasonable value manually by doing "synclient FingerPress=100". I found it also better to increase the values for FingerLow and FingerHigh a bit.
Of course you will want to make the setting permanent, so that it will survive a reboot. In that case you need to put the setting in /usr/share/X11/xorg.conf.d/50-synaptics.conf (see e.g. How to configure the touchpad middle click? how to do that).
I hope Ubuntu can improve auto configuring of different type of synaptics touchpads to a next level, for most users it is hard to solve.