Why would a car run great but cut out sporadically at 25-35 mph?

CHANGE YOUR PLUGS.. YOU PROBABLY HAVE A BAD PLUG OR A WET ONE

I doubt it's spark plugs, but it's possible. This problem happened to me a few years ago, and initially I thought it was speed related but it turned out to be throttle related.

There's a sensor on vehicles these days called a Throttle Positioning Sensor (TPS), and these wear out and develop a "flat spot" on them. When you have your throttle on that flat spot, the computer doesn't know where your throttle is positioned and your engine will hesitate and then "kick", and with a stick it can be pretty violent.

As you're accelerating, and as the car gets to that 25-35 zone you describe, give it more gas than you usually do and see if it behaves normally. If it does, I'd bet money it's that TPS.

As I recall, the TPS was about $80 and a real easy fix. It's located right on the side of your carb.