Raj tells Penny and Leonard he straightened his hair because Howard was his first friend and the coolest person he knew. In The Staircase Implementation (2010), there are flashback scenes in which Howard's hair is curly and Raj's hair is straight and styled like Sonny Crockett from Miami Vice.
Sheldon says at the beginning of the episode they will use Decision Science to make plans for the wedding, but they are never never depicted using Decision Science, only random assignment.
At the end of Raj's presentation at the observatory, a guest asks him, how life could be detected on "these planets". Raj was talking about Enceladus and Europa. Both of them are moons, Enceladus is a moon of Saturn, Europa is a Jovian one.
Sheldon goes out of his way to avoid a first dance at their wedding; however, in The Agreement Dissection (2011), Sheldon has no problem dancing with Amy in public, thanks to the southern custom of Cotillion which taught him the rumba, box trot, and the cha cha. He considers himself "an excellent dancer".
When Sheldon and Amy are discussing their wedding, Amy says she will arrive in a Little House on the Prairie style horse drawn buggy, and Sheldon continues that she will be met by an honor guard of storm troopers. After a discussion about how jarring it might be, Sheldon says Amy can pick the ushers. However, on their list 'greeting party' is also listed, which would make more sense for what they were talking about.