Don't test your chips with an oscillator circuit. Test them with just the pot by connecting the pot between +5 and gnd. Connect the wiper to one of the inputs. Adjust the pot from one end to the other. Monitor the output and as soon as it changes state, measure the input voltage. Adjust the pot both ways, from +5 to gnd and from gnd to +5. Compare the results to the datasheet.
+1 but I already suggested that and, apparently, the Schmitt thresholds are at 3.6 and 1.1V which is in line with typical values.
74AC series is a bit special, it can sink AND source about 30ma
other 74 series generally only sink OR source, the oposing bias is simply done with an internal pullup/down resistor.
74AC does appear to be able to drive higher currents but are you sure other 74 series can't both source and sink current - pulling a few 74HC14 datasheets at random suggests ± 20mA is typical.
It is of some relevance though because the output needs to be able to sink the capacitor discharge current as well as source the charge current - which brings up another weakness in this design. At either end of the potentiometer range the cap is effectively connected directly to the output, so the current spikes might be quite large. Probably not much of an issue in practice but it might be better to stick a couple of fixed resistors between the ends of the pot and the diodes.
However this is a "I need a quick PWM on a breadboard" circuit, not something which is "production ready" - I wouldn't get too hung up about the details.
We've had two working with 74HC (mine and rdl's) and one with 74AC (alsetalokin4017's) and with 74C (also alsetalokin4017). RyanG tried with HC but I think we can stop telling him it won't work without a 74AC14.
At this point I think trying a different breadboard would be useful.