Shapefile and vector file don't precisely overlap when plotted

Question

I want to plot a shapefile over a raster file in R but I can't make them overlap perfectly: the raster appears to be rotated of few degrees counter-clockwise. Is it a problem with the projection?

Please consider the following MWE

library(raster)
library(rgdal) 

# Download from http://biogeo.ucdavis.edu/data/gadm2/shp/ITA_adm.zip
shape_file = "ITA_adm1.shp"
# Download from http://sedac.ciesin.columbia.edu/data/set/gpw-v3-population-density/data-download
# Setting Geography: Country, Italy; Data Attributes: Grid
pop_density_file ="w001001.adf"

italy_map <- readOGR(dsn = shape_file, layer = "ITA_adm1")
italy_map_dens <- raster(pop_density_file)

colPal <- colorRampPalette(c("white", "red"))( 500 )

par(mar=c(0,0,0,0))
plot(italy_map_dens, xlim = c(6.70, 18.32), ylim = c(35.2, 47.6), axes=FALSE, box=FALSE, legend=FALSE, col=colPal)
plot(italy_map, xlim = c(6.70, 18.32), ylim = c(35.2, 47.6), border="grey", add=TRUE)

Answer 1

Apparently there was a bug in the rgdal package. My problem was solved after I updated it to version 0.8-12.

Answer 2

It does appear to be a problem with the projection. You need to find out the exact projection of both datasets, and convert one of the datasets to the projection of the other dataset.