The IAC valve has SOME engine control up to about 2K RPM. It really does
sound as if yours is sticking. The IACV is also one of the things that
OBD-II won't detect with a direct code.

Doesn't the IAC only deal with engine idle?

My problem is while accelerating, when the engine is under load. Just
after shifting is most common, also when pulling away from a stop it
happens a lot too.  Less common but still occurring is when pulling up a
hill or accelerating on the highway.  Maybe twice in the past 6 months
I've had a rough idle for a few seconds, but that's all.

The oddest part about the problem is that it will not occur for a while,
even if you really thrash the engine.  But other times you can be really
gentle with it and it will hesitate every time you try to speed up.

No codes? It sounds like the IAC valve is dirty/worn.

There was a code a few weeks back, p0102 MAF/VAF Circuit low input. And
my mechanic said I needed a new MAF at great expense.  Didn't improve
the problem though.  I've had no other codes since.

Actually... if it's a HIGH idle, it may be related.

Sometimes ymptomatic of a bad wiring harness ground or engine to body
ground.

Try doing a tug test on all engine wiring harness while it's idling, may
point out a connector that's making bad contact

Are you sure there's no codes stored?

I have a 98 Windstar 3.0 with 128k miles on it, and over the past few
months it has had a problem with hesitation and bucking.  The problem is
intermittent.

My mechanic has diagnosed a few things so far and a lot of money has
been spent on 'repairs' but nothing he suggests fixes the problem.  I've
now taken it back from my mechanic and his "shotgunning" repair
technique in order to try and diagnose the problem myself.

So far I've replaced the Throttle Position Sensor and the Camshaft
Position Sensor, and while that seemed to fix it for a day or two, the
problem came back.  (It's intermittent nature means it can run fine for
days).

There seems to be no rhyme or reason to the hesitation, it can happen
when you're pulling away gently, or when you're cruising at highway
speeds, or during a shift, pretty much any time.  Turning overdrive off,
or keeping the transmission in 1st or 2nd makes no difference.  Also you
can drive it really hard sometimes without the problem manifesting at
all.  Often I'll drive it hard 10 miles to work and it's fine, then it
will act up on the way home with about 3 miles to go.

As good as I can tell it feels like the engine is cutting power to the
injectors or plugs all at the same time.  And the loss of power can last
from a fraction of a second to a whole second before it recovers.
Sometimes you just feel a bit of spluttering as though only a single
injector or plug isn't firing.  I thought it might be a transmission
problem, but I'd imagine that the revs would climb while the
transmission slips, and that's not happening.

I've also had poor idling on occasion, but it's very uncommon, so may
not be related.

Any ideas what to try next?