The odd bit is R3. In series with R1, it forms a 250 Ohm resistor in parallel with the cap during the discharge phase, giving a RC time constant of 25us, but as the PIC internal oscillator speed is 4MHz (1 MIPS), that's only 125 instruction times for 5*RC, so it will seriously compromise the measurement resolution, and swamp the unknown resistor if its over about 30K.