I use AutoDock on EVERY ship I own. I can dock just fine manually, I've done it enough times, I just don't like doing it any more. Auto-dock, and launch, being a bit flaky with the Cutter was the norm for years. However, some time ago a bug was fixed on the Cutter - something to do with its manoeuvring thrusters not working as they should - which meant it docked, and launched, far more reliably than previously when using the DC. It still has the odd wobble, but it has always quickly recovered and exited the station just fine. I'd say that the station docking approach is slower these days than it once was, that seems to be the case for all the ships I've flown recently, but it has been less prone to issues.
I've had to wait for several minutes before my ship has actually exited the station before, however, this was usually when there was busy AI traffic. It used to be that if you say logged into the game while docked, then didn't leave right away, the game would spawn more and more AI ships, causing jams when you finally did try to leave. It doesn't appear to do this any more, at least it hasn't for me, so that's another little issue that's been addressed. For this to happen when there's little or no other traffic is odd. However, now you mention it, a few days ago I was leaving a station using the AP and my ship did just "park" as if waiting for another ship to enter / exit the mail slot. No other ship appeared for a good minute or so - nothing near me about to leave that wasn't also waiting, and certainly no incoming ships on an approach to the mail slot. So, I just took manual control and quickly exited the station. I just put it down to being a minor gremlin in and otherwise fairly robust AP.