Something very fishy there with respect to the voltages at Q3. Notice
that Q3-b is fed from Q3-c, so the potential there should be lower than
Q3-c in any event. And if Q3 is OK and wired in correctly, since Q3-e
is grounded, you can't reasonably have Q3-b much more than 0.7V above
ground. It's just a forward-biased junction. So as a start, look for
problems around Q3! Remove Q3 from the circuit, and check the voltage
at the bottom of the 10k resistor...should be nearly the same as the
battery voltage. And at the junction of the 560k and the 100nF, should
be just slightly lower. Then if you ground the bottom of the 10k, the
junction of the 560k and the 100nF should be zero volts. If it's not,
perhaps the 100nF is bad (leaky or shorted). I'd say the 100nF (which
is indeed 0.1uF) is way larger than needed in this circuit--100pF would
likely be large enough.

The description says it's a "regenerative" circuit, but I'm not seeing
any significant regeneration! Looks like a simple RF amplifier
followed by detection in Q3's base-emitter junction, and Q3 amplifying
the audio.

100uH and 10pF would tune about 5MHz, though stray capacitance and
parasitic capacitance in the coil will make the net capacitance
somewhat higher. 100uH and 120pF would tune about 1.45MHz, just the
upper end of the medium wave broadcast band. I'd suggest you try for
more inductance and/or more capacitance in the tuning system. For a
quick trial, just parallel in 100pF or so; the tuning range will be
limited but at least you'll be in the MW broadcast band more solidly.

Cheers,
Tom