LightDM fails to start after removing nvidia-prime

you need to purge to revove the configuration files not just remove. This is incredibly important when dealing with drivers and kernels. (in short use "apt-get purge" not "apt-get remove" to deal with lower level packages)

I understand, and that is eventually what worked for me. Even so, IMHO there should have been a warning on remove, explicitly saying that not purging will make things go bad.

Status changed to 'Confirmed' because the bug affects multiple users.

Purging is not the answer here.

First, given that the package auto-added its binaries to lightdm.conf, it should make sure that those binaries that are not present anymore in lightdm.conf when removing them from disk. This is not a config file that is harmless if left over, this is a config that is broken because the binaries are no longer present.

Second, even after purging, lighdm.conf still contains the reference to the wrong binaries, so, purging doesn't help AT ALL.

This is a piece of code from the postrm script, which should do the right thing:

lightdm_orig_conf=/etc/lightdm/lightdm.conf
remove_hybrid_script () {
    # Precise only!
    if [ -s "$lightdm_orig_conf" ]; then
        # Get the file
        lightdm_orig="$(cat $lightdm_orig_conf)"
        echo "$lightdm_orig" | \
        sed "/.*display-setup-script.*/d" \
        > "$lightdm_orig_conf"

        lightdm_orig="$(cat $lightdm_orig_conf)"
        echo "$lightdm_orig" | \
        sed "/.*display-stopped-script.*/d" \
        > "$lightdm_orig_conf"
    fi
}

The problem is that this script is limited to Precise:
        os_release="$(lsb_release -cs)"
        if [ ! "$1" = "upgrade" ]; then
            if [ "$os_release" = "precise" ]; then
                # Remove the display-setup-script line
                remove_hybrid_script
            fi

This has two problems:

1 - on the preinst (!) script this check is done differently:

add_hybrid_script () {
    if [ "`lsb_release -r -s`" = "12.04" ]; then
        # Precise does not support separate config files
        if [ -s "$lightdm_orig_conf" ]; then

This means that if for some reason lsb_release is 12.04 but the name is not precise, then the undo doesn't really work.

2 - People can upgrade from precise to something else. So, if they were running 12.04 when they installed nvidia-prime and then upgraded to trusty or whatever and remove nvidia-prime, the lightdm.conf file is left broken.

Please make sure that you undo whatever was done, regardless of the currently running distribution. Also, if you are going to check for a specific fact for doing and undoing, it should be a the same fact, not a "it should be equivalent" fact.

Finally, the code in the preinst should actually be in the postinst, otherwise there's the risk that something might fail while unpacking and the lightdm.conf fiel will be left in a broken state.