I have a genuine Honda iPod controller for my iPod in my Accord Euro, and it does the same things. I use an iPod Classic 6.5 gen (current model, 120G HDD), and if it's been powered down for some time - perhaps 2 days or more - it takes a long time to wake up; by the time it becomes responsive, the Honda controller reports an error about the device.
To get around this, I always switch to tuner mode before I turn the car off, so when I start the car again, it's not trying to read from the iPod immediately.
As for the stuttering/pausing, I have that from time to time as well, and have attributed it to the iPod disk spinning up, seeking and buffering the track. Sometimes the iPod becomes unresponsive as well, and needs hard-rebooting followed by playback with headphones inserted before it'll play music. Bloody annoying.
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