I learned in this answer that touch screens with a glass front are generally more sensitive and accurate than those with plastic fronts. This corresponds with my personal experience.
However, is there a way to bring devices with plastic fronts up to the accuracy and sensitivity levels of those of glass? What would this require?
There are many ways of constructing a PCAP touchscreens and some of them are entirely independent of the glass material. In effect the touchscreen is a film attached to the coverglass (or plastic) so as long as the material does not mess with the electric field projected by the capacitive terminals the touchscreen is perfectly happy. On the other hand glass has better permittivity than most plastics so you get roughly similar capacitance with 2-3x thicker glass than you would with plastic. Whether or not this is significant depends on the application. General trend is to create as thin coverglass as possible and thick glass solutions are reserved more to vandal-resistant public displays.
Some touchscreens are actually integrated to the LCD display, which is what Apple does.
Without going to gritty details, your touchscreen requires two terminals, between which the capacitance change is sensed. Depending on construction these may be separate films with insulating layer in-between, single layer constructions with some clever routing, exploiting LCD display cells as a terminal etc. Most basic of these are organized as a crisscross pattern with separate layers, more sophisticated use diamond patterns that etch jumper bridges to "hop" over opposing terminals and so on.
In fact you don't need the glass at all for the touchscreen to function. Except touching the touch screen would "short" the traces.
If you're interested in touch technology in general, Geoff Walker has quite comprehensive presentations on the subject here: http://www.walkermobile.com/PublishedMaterial.htm