Hi,
Personally, I recommend a 100k (or even higher) pulldown resistor directly from the PICaxe programming input pin to ground, (which admittedly is NOT in the Manual). That still allows the PICaxe to boot correctly, but allows a few other "tricks" such as enabling the internal Weak Pullup resistor on that pin. The problem with 10k is that you might form a potential divider with the "22k" programming resistor and get erratic (or even no) programming. Putting the 10k on the "PICaxe" side of the 22k is probably the
second most common "gotcha" on the forum.
Cheers, Alan.