According to the producers, the role of Amy's father Larry was not written with the plan or idea of Teller playing the part. It was only upon the script's being finalized when the producers realized that Teller would be the perfect person for the part.
The running gag of people talking to Mr. Fowler, only for Mrs. Fowler to cut him off before he can speak, is an in-joke to Teller's magic/comedy act with Penn Jillette; Jillette is the more loquacious of the two, and Teller rarely, if ever, speaks. His silence stems from his youth when he performed at college frat parties; he found that by refraining from speaking, the audience was less likely to heckle him and more likely to pay attention to his act.
Mark Hamill does have a dog in real life, but it is not the dog used. His actual dog, who's named Millie and not Bark, was not allowed to be used per union rules. Therefore he used an acting dog, and made up the idea of the fans naming his dog online as for why it's named "Bark Hamill".
Chelsea Hamill: Mark Hamill's daughter appears as the wedding guest in a red dress when Howard goes to tell Wil Wheaton that he's been replaced as the wedding's officiant.