I understand what you suggest about too weak a pullup, I had wondered about that myself, but I am unsure of how high a pullup current the pin should see, in other words how "stiff" the pullup should be. The spec sheet says the source current max on any port pin is 25mA. My gut tells me the reed switch should be able to handle that at 5vDC but I would hope that it would not be necessary to max out the current to mask the noise.

Any thoughts?
The 25mA source/sink current doesn't apply here. That's what the pin can source or sink when it's configured as an output - that's not what you're doing. When the pin is configured as an input you can, in this case, pretty much ignore the current flowing into it (it's about 100nA on the 16F722).

Your pin is held high, at 5V (?), by the 47k pullup. The only current that's flowing is the 100nA (max) into pin and any leakage current thru the switch. The reed-switch, when activated, pulls the pin to GND, ~100uA is flowing down thru the pullup resistor causing a voltage drop of ~5V across the resistor, the input is now low. All is well, on the drawing board - and in your testup.....

Que long leads, aka antennas. With such a weak pullup as 47k it doesn't take much noise on the long wires to start "yanking" on that logik level '1' provided by the 47k resistor.

Although there are reed-switches available (I quickly browsed Digikey) that can only handle around 100uA, some 1mA most of them are capable of 100mA or more. If I were you I'd lower that pullup by an oder of magnitute (or two even) and add a small cap as per previous suggestion - then try again. Even a 470ohm resistor will still only give ~10mA thru the switch.

/Henrik.