first, the Read-Modify-Write issue (from http://www.voti.nl/DB038/DB038-1-1.pdf, p51):
PICs use a funny IO architecture where a reading of a pin always returns the current external level of the pin, which can be different from the last value written to a pin, even when the pin is set as output, for two reasons:
• PIC instructions execute in a 2-stage pipeline, and for IO pins the read part of the next instruction takes place before the writing of the previous instruction.
• The load on the pin can be too high for it to reach its 'desired' level. This can easily happen (for a short time) when the load is capacitive, but it can also happen with a static load that is well within the normal operating specifications.
All PIC instructions that modify some bits in a byte are read-modify-write instructions, so when for instance two consecutive BCF (bit clear) instructions are executed on the same IO port the second instruction can ruin the effect of the first because of the first of the two reasons. Actually a BCF instruction (and a lot of other instructions, like INCF) on a port can ruin any previous setting of that port because of the second reason! It should be noted that the first reason occurs far more often, and can be avoided by placing a NOP or another instruction between any two read-modify-write instructions on the same IO port. But to really avoid all problems it is advised to allocate a separate register, do manipulations on that register, and copy it to the port register after each change. This technique is called a “using a shadow register”.
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Next: RC delay. When you change an I/O pin connected to a non-trivial amount of wire always wait a reasonable amount of time before expecting the result. In the absense of another source of 'reasonable': find out what seems to work, then double the time.
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Last: debouncing. AFAIK 50 ms is a reasonable upper limit for the bounce time of a switch. When your sample interval is longer than this time (you use 100 ms), you have no bounce problem. The proof is left as an excercise to the reader :)
Best Answer
There's a schematic of the keypad in the old Student Manual at the end of Chapter 15. Not sure what the disembodied U4c bottom-centre means, but it can't be that hard (famous last words!)
Update on 20 June 2018:
The author, Thomas Hayes, has been away on vacation but has got in touch to say he will put up-to-date details of the keypad on the Learning the Art of Electronics website. It is different from the one in the old Student Manual as he has re-designed it with a microcontroller in place of the many IC's of the older version, to do keypad scanning, switch de-bouncing and display.