keyboard problems on Dell Latitude E6230

I'm having problems with the built-in keyboard on Dell Latitude E6230
laptops and Linux 3.12/3.13 kernels:

- sometimes the keyboard just keeps sending the same key code, as if
  the key was held down permanently; sometimes that can be cured by
  pressing ^C or something, but often only a reboot fixes it

- sometimes the keyboard just stops sending key codes; only a reboot
  fixes it

This issue has plagued me since Nov last year when I got my first E6230.
Last week I got a replacement machine, but it too has the same problems.

Since I haven't seen this problem with any other laptop under Linux for
the last 15 years or so, I have to conclude that there's some HW issue
with these machines that the Linux kernel doesn't handle.

Any ideas?