The scene where Maggie puts her tongue on her booster seat and it gets stuck there, is a reference to the iconic scene from the 1983 Christmas movie, A Christmas Story.
Moe claims he is a snake handler, and this is the only episode to mention this. Snake handling is a controversial aspect of the Christian faith, where it is believed faith will prevent snakes from attacking. It is often preached in the Appalachia region of the United States. The Supreme Court case Bunn v. North Carolina revolved around this, saying that state legislatures and county governments can pass laws prohibiting the use of poisonous snakes in church sermons due to the potential for real-world danger.
God, who makes his first appearance in this episode, is the only character in The Simpsons to have five fingers on each hand.
Apu, Skinner, and Moe were all volunteer firefighters in this episode. They would later also be volunteer firefighters in "Crook and Ladder." And Apu, Moe, and Ned Flanders were also volunteer firefighters in Brother's Little Helper. Luann van Houten was shown as being a member of the Volunteer Fire Department in this episode.
Some fans of The Simpsons have held parties on June 5th and calling it "The Feast of Maximum Occupancy", in reference of Homer's excuse to get out of work by making up a holiday by looking at the safety warning at Moe's Tavern, which read "Maximum Occupancy, 65". The June 5th party date is a reference to the digits 6 and 5.
At the end of the episode, God mentions that Homer has to wait six months to know the meaning of life, because Homer will die. Homer later dies for a few seconds in "Homer's Triple Bypass". Ironically, that episode also has Homer dreaming about what is implied to be Hell and referring to it as a "wonderful dream."
Despite this, God soon tells Homer the meaning of life, but the closing credits start before the audience can hear it.
This episode shows how Homer was born. Unlike Bart's birth in "I Married Marge", Lisa's birth in "Lisa's First Word", and Maggie's birth in "And Maggie Makes Three", Homer was seen being born from inside the womb and not from outside the womb. You can clearly tell this by the womb's shape at the beginning of the scene, the amniotic sac breaking after Homer's dance, the umbilical cord that's attached to Homer before he pulled it out from the womb, and a hand (possibly the surgeon's) pulling Homer's legs out of the womb while he grasps onto it as he gets delivered.
However, just before the rest of Homer gets delivered after his legs, the scene cuts to the present, where Homer, grabbing onto his bed's headboard (similar to how he grasped the womb when he was delivered), is getting pulled out of bed by Marge. This reveals that Homer was dreaming about his birth, and Marge was pulling on Homer while telling him to wake up, similar to how the surgeon's hand pulled Homer out of the womb at the end of Homer's dream about his birth.
This episode also reveals that Homer was a breech baby and he was born via a breech delivery during Homer's dream about his birth. You can clearly tell this by the surgeon's hand delivering Homer's legs first.
Sloth: Homer misses church in order to sleep in and lounge around the house, and is shown to be very reluctant to get out of bed.
Gluttony: Homer uses an entire stick of butter in his moon waffle and remarks to himself it is "fattening". Homer also uses his standard "Mmmm", which he has repeatedly used, often when indulging himself.
Greed: Homer finds a penny. While that act is not in and of itself sinful (and actually virtuous to be saving and thrifty), he considers that it marks a new red-letter day in his life, superseding the days he celebrated dancing in a spray of beer from a disabled truck (also gluttony) and his own wedding day.
Wrath: Homer slams his hands on the wheel of his car when Ned refuses Homer's orders to stop pestering him. Homer is also expressing anger through his loud dissatisfaction of the suit he often wears on Sunday, calling it "itchy" and "one size fits all, my butt!"
Envy: Homer is upset that Marge always takes someone else's side, including Flanders, the water department, and God.
Lust: Homer reads Playdude on the couch, and tries to pressure Marge into "coming to bed" whilst she is praying.
Pride: Homer invents a new religion that caters to his own whims. Just as Pride is often believed to be the source of the other deadly sins, in this case, Homer's pride in creating his own religion also led to him committing the other sins. In addition, Homer's pride manifests verbally when he says "Everyone is stupid except me," directly after which his house catches fire. This is the last of the seven sins that he commits, and the fire immediately afterwards can be considered an allegory for the end of life; a.k.a. the Fires of Hades.
When Homer skips church and watches TV at home, he watches The Three Stooges (obvious due to a Curly-like cry coming from the TV).
When Homer dances in his underwear, it is a parody of the dancing scene from Risky Business, although the song in the film was Old Time Rock & Roll by Bob Seger.
Playdude is a parody of Playboy.
At the end of the episode when Homer sets the family home on fire he is rescued by Ned Flanders, however it is a Sunday, therefore Ned should have been at church. Even very religious people will skip church sometimes. Also, most churches have more than one mass so Ned could have went earlier or later. Similarly, some sects of Christianity split the church into "wards", so as to avoid overcrowding by having everyone at church at once; Ned's "ward" may have attended earlier. It's also possible that Ned was late and was on his way there when he saw the fire.
God is the only character to have five fingers on each hand, but only has four on each hand (like most Simpsons characters) during the scene at the end of the episode.
When Homer is opening up the waffle iron, the machine's legs disappear for a frame.
When Marge says, "Kids, your father doesn't really mean that," Bart is in front of Homer, but immediately afterward, Bart is suddenly behind Homer. Then, when Marge asks, "Homer, are you actually giving up your faith?" Bart is in front of Homer again.
When the house catches fire, it spreads to the two strands of hair atop Homer's scalp, which burns them and awakens Homer from his snoozing. When Homer stands up, his hair has already regenerated.