On the Century-2000 equipped Bonanzas I fly, there's an interesting
trim problem with the AP, which is basicly that it doesn't trim.

Engage the AP while you're being vectored for the ILS and let it
fly the approach, as you keep reducing power to slow down and then
track the GS. As you slow down, you should be dialing in nose-up trim
(and, indeed, the AP prompts you to do this, but if you're not paying
attention, you can miss the flashing light).

Now, at DH, click off the AP to hand-fly the landing. All of a
sudden, you've got a fistfull of yoke trying to pull your arms out of
their sockets until you get the trim fixed. Even worse if you didn't
see the runway and clicked off the AP to execute the missed.

Of course, the AP is performing as designed, and it's the pilot who's
unairworthy, but it's a common enough mistake that I've got to believe
it's a design flaw in the system. If nothing else, it should have a
more obvious alert than a small blinking light outside of your main
visual scan. Like maybe a mechanical arm that smacks you upside your
head with a rolled-up sectional while a synthesized voice says, "Trim
up, trim up".