The province of Liverpool includes the city of Liverpool. That I know is correct. Liverpool is at the southern edge of Lancashire, and the map border for the province represents, to the degree possible given the limitations of the area represented by a pixel, the southern border of Lancashire. As such there is no "glaring error" in the province setup. Considering we are talking about a province border of maybe 3-4 pixels wide at most, adding even another row of pixels would put the southern boundary of the province well into Cheshire.
The port icon projected onto the map as shown in screenshots, however, is displaced to the north. Liverpool is not the only province to show this, many port icon locations on the map are not exactly where the city which the province represents is located.
There are, however, valid reasons for this to happen. Bear in mind that you need to be able to have enough space for the various incarnations of the port icon as well as clarity to tell if there are ships docked in the port or not. This means that placing the icon at the exact geographic location of the port on the map may actually make the map less useful for depiction of the activities at said port, since it may result in overcrowding in some areas of the map if the province density and the cities chosen to be the headquarters of the provinces are close together.
For those who feel that this is somehow a travesty to geography, as in EU3 and HoI3, it is a simple matter to tweaking the coordinates of the icons relative to the map in the relevant plain text file.
And as for the Alsace issue, what we are talking about is a small area in the northwest of Alsace that projects into Lorraine. I found that when the map was reduced to the size of HoI3 ingame map, the resulting border was very disjointed, IIRC even creating a small split in the Metz province, hence the decision to keep the provinces of Strasbourg and Colmar relatively clean without the projection to the northwest. As qwerkus notes, since this is the Clausewitz engine one can easily mod to adjust to a bit more "historically accurate" border in any part of the map, but the result will be to change maybe half a dozen pixels at most, and create a border that not only looks more jagged and angular between Metz and Strasbourg, but geopolitically in game will mean little in the effect that both provinces will be part of the German-occupied Alsace-Lorraine.
