When Elder Dutson baptizes The Swede, he doesn't pronounce the established prayer in use since the Church's establishment in 1830, as published in Doctrine & Covenants 20:73: " Having been commissioned of Jesus Christ, I baptize you in the name of the Father, and of the Son, and of the Holy Ghost. Amen."
The song "When I Am Baptized" that Ezra (and later, the Swede) sings, is an actual children's song used by the LDS church. However, it was not written until the 1980's, and not copyrighted by the Church until 1989.
The landforms and vegetation are not correct for Central and Eastern Nebraska along the Platte River. There are a few low bluffs along some portions of the Platte, however the scenery depicts continuous, fairly steep bluffs, sometimes on both sides of the river. Also depicted are large forests of both deciduous and coniferous trees. No such forests existed along the Platte River or near the Platte River. It is stated that the crews went in search of timber for ties, a reasonable distance from Hell on Wheels. However the plains of Nebraska do not have hardwood forests; oak and other hardwoods performed best for railroad ties. The Union Pacific at this time relied on hardwood timber from the East, in particular Minnesota. Cottonwood was found on the banks of the Platte but it was mostly unsuitable or too soft for ties.