Record image courtesy of the Rick Payne Collection via dadric's attic.
Heigh Ho follows Dig-a-Dig-Dig on Side B of the first disc of the three-record set. Of course, we know they also run back-to-back in the film; the dividing point between the two occurs when we see the clock strike five and Doc calls out "heigh-ho!"
Both record and theatrical-release of Heigh Ho are identical up until 44 seconds into the song. In the movie, Dopey has just put the vault key on the nail, and he runs to catch up with the others on their homeward journey.
The record version then continues on with about 18 to 20 seconds of a whistling melody which is not included in the movie sequence. Animation for this segment was planned, but due to time considerations, it was cut.
The remainder of the "Heigh-Ho" song is the same as what we hear in the film when the Dwarfs march home to the cottage for the first time.
This whistling melody, however, was not left out completely. It was brought to my attention by Snow White enthusiast, Nunziante Valoroso from Italy, that it did indeed make it into the final movie. It was simply moved to the last reel of the film and occurs in the scene right before the animals arrive at the mine to warn the Dwarfs about the Witch. They whistle the tune while they're pulling a mine cart.
After comparing the other songs from the 1938 record set with what is in the movie, I happened to notice another minor anomaly. At the conclusion to One Song, when the Prince is singing to Snow White from below her balcony, she sends a dove down to him to deliver a kiss.
The dove blushes while sitting on his hand. In the picture, a dove "cooing" sound effect was inserted at this point. On the record album, it was not. All of the other dove intonations, though, do seem to be in place on the soundtrack disc.
Screen captures and audio excerpt copyright Disney. Included here for historical documentation purposes.