I have an '88 CRX HF with 175,000 miles on it. The engine shudders
pretty violently when the accelerator pedal is held at a particular
spot in its range of travel. It occurs in any gear, at any RPM. It is
more noticeable at lower RPMs probably due to the lower inertia of the
reciprocating mass. If I press the pedal down past this point, say
~1cm, it goes away. Similarly, if I let up on the pedal the same
distance, the shaking also stops.

Car has new plug wires, new O2 sensor (Bosch), new distributor, and a
MotorVac flush service done. Its also had a new timing belt put in and
a valve adjustment done in the past 25k.I suspect it could be the
throttle position sensor, but I'm not familiar with its construction.
Is it possible that it could have worn out in this spot and is sending
bad/no signals? Any other ideas?

On a related or unrelated note, the car also idles erratically,
sometimes too high (1100RPM), sometimes too low (250RPM), sometimes it
bounces between 900-1100RPM. A Honda tech told me my accelerator cable
was too tight. I haven't fooled with that yet.