I have experienced the same on my Raspberry Pi’s with the same GrovePi+ board (newest version).
-When plugging in the adapter with the plug on the Pi, the reset LED lights up, need to run “avrdude -c gpio -p m328p”
-When taking out the adapter from the wall socket and plugging the adapter back into the wall socket, the Pi runs fine! So it seems to have to do something with how the Pi B takes in the power at first. I can reproduce both cases a 100% consistently.
-With Dexter Raspbian image, the reset LED lights up as well, but eventually stops doing this (I assume there is a script that runs “avrdude -c gpio -p m328p” on your image) but with the normal Raspbian image, it doesn’t go away until after running “avrdude -c gpio -p m328p” so I put it in the rc.local script, then when the Pi is done booting the reset LED is off and the GrovePi+ works without the need for user intervention. Though I think running the script as a high priority /etc/init.d/ script would be better when you want the Pi to boot automatically with other scripts needing the GrovePi board. If those scripts would run before the rc.local script and rely on the GrovePi board, it might cause problems.
No problems whatsoever.
I have just added an init.d script, but it still is pretty slow in enabling the board (i.e. turning off the reset LED). What did you use in your Dexter Raspbian image to reset the board to the working state? The Raspbian Jessie image boots way quicker, though it takes about 22 seconds for the reset LED to go off. On your image it only takes about 10 seconds, while the whole boot sequence is a lot slower (as it has a lot more services booting than the cleaner Raspbian Jessie installation), so there has to be something going on before even the init.d sequence is starting.