While it is possible to report bugs without specifying a package (as you've discovered), bugs reported that way virtually never have any progress made on them until a package gets specified.
So it's best to report a bug against a specific package whenever possible. You shouldn't randomly guess, but it is OK to report a bug against the wrong package if you had reason to believe it was the most likely package.
If you had to report this bug with no further information, I'd recommend reporting it against
gnome-settings-daemon (remember, Unity is a shell for GNOME, a Unity desktop is GNOME). Probably that is what's preventing the setting from being applied correctly some of the time. This is (most likely) the package that should be applying the setting at login, and is not doing so properly.
If you happened to have KDE installed too, and it happened there as well (even when no GNOME login had taken place since reboot), then
xserver-xorg-input-mouse, which provides mouse input functionality to the GUI, might potentially make more sense.
gnome-settings-daemon is your best bet, right now.
It's best to start a bug report with
ubuntu-bug but if you already filed the bug on Launchpad, you don't have to report it again (unless asked to do so). Instead, specify
gnome-settings-daemon as the package. Once the bug report is targeted against that, run
BugNumber is replaced with the bug number on Launchpad. This will automatically collect and attach (at least most of) the technical information that would have been attached had you started the bug reporting process by running
If you wish, feel free to subscribe me to the bug. (I'm not a triager or developer though; I might not end up helping any.)