The titular storyline plot starts with Penny being unaware that Las Vegas weddings count as actual marriages. Yet in The Countdown Reflection (2012) when Howard and Bernadette were trying to get married before he went to space, Penny herself suggested getting married in Vegas, including saying she knows several people who got married there.
When Sheldon sits down on the couch with Mike, his tie covers the buttons on his shirt, then in the next shot is drooping more off to the side. Then, when Bernadette storms in to force them to apologize to Howard, Sheldon's beer switches hands between shots.
When the annulment papers are on put on the table and Penny says, "Let's get this over with!" she turns to look at Leonard. In the next shot, she's looking straight down at the table.
Howard's mother would never have been allowed on a mule at the Grand Canyon. There's a strict weight limit requirement to ride them for exactly that reason.
Penny states that they went to a wedding chapel. Even in Vegas you have to get a marriage license before you go to a chapel. But Penny never mentions they went to the Marriage Bureau first or anything about getting a marriage license.