Broken cam as in the main engine cam?
No way! The engine would destroy itself in a few rotations under that problem. Maybe he meant a cam on the carb linkage? No - he said pull the valve covers to look, so he must mean the real cam...wow...that's silly! Even a worn lobe doesn't do this generally.
While it's not a bad idea to pull the covers and turn the engine over while watching them for seemingly decent operation, I would more suspect something on the order of my favorite problem of the season - a blown head gasket.
Under acceleration only sounds to me a little more like a badly adjusted vaccum or sticking mechanical advance though.
Go through the basics - look at everything in the distributor, make sure the mech advance seems to work cleanly and that the rotor is in good shape and not wobbling. Make sure the distributor cap doesn't have any tracks in it or any cracks. Make sure the vacuum line to the vac advance is connected and not leaking. Double check the timing. Check each plug wire for contact with another or a sharp edge on the engine. Somebody over on CF (I think) recently had a nightmare from some simple bad plug wires - but they were high grade ones.
Those backfires have probably wiped out your carb's power valve that give you good mid throttle response and will result in a surging and falling of rpm at idle. That alone can cause a temporary lean out under acceleration which can cause detonation - but not usually a backfire.
When you do look under the valve covers, look at each valvespring to see if any look shorter. An unseating intake valve from a collapsed spring can cause this. You also have the pleasant options of bent valves, bent pushrods, badly failed valve guides - a whole WORLD of messy grief!
If you have a vacuum gauge, note how it acts under idle, when revving it, etc. A lot can be told regarding valve seating and such from a twitch of a few inHg or a very low reading. The Chilton manuals and other such references usually have a little chart on what each vacuum condition may indicate.
If all of these "hour long checkup" things yield nothing, run a compression test to see if one of the cylinders is blowing its stuff into another from a blown head gasket.
Other evil things could be a worn or stretched timing chain, resulting in your apparent timing being much greater than you thought from the marks with the timing light. If it's too far advanced - it backfires, if it's too far retarded - it afterfires.
BTW, are there any other symptoms? Overheating? Air blowing out overflow?
