My Model 29 is a nickel 6 1/2" in a wood case. Serial number is N4569xx and I think it was made in 1978. Am I right? Can someone explain what the infamous "4 screw" gun looks like as compared to the one I have (with 3 screws in the side plate?).

You can do a search on this forum for pics of 4 screw guns.
So you know what to look for: the 4th screw is just on the front of the trigger guard, at the curve where the guard transitions to the frame under the yoke.

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The 4th screw was dropped many years before yours was made.

Model 29s with a 4-screw frame have three screws in the side plate and the cylinder stop plunger screw (or, fourth screw) in front of the trigger guard. The engineering change to implement the improved cylinder stop with the elimination of this screw was issued by S&W on November 28, 1961. It took about seven months to implement the change for this model with three screw Model 29s being first shipped in mid-1962.

You are correct about your 29-2 being shipped in 1978.

The photo below is of an early .357 Combat Magnum. Click on the photo and look in front of the trigger guard and you will see the fourth screw.

Bill