When Nick and Loretta come into Cheers to get the adoption papers signed, Sam is behind the bar, and the front table is empty. In the next instant, Sam is in front of the bar asking Carla if she has something to say to Nick. When Carla goes to answer Nick, he and Loretta are sitting at the table, and both have a drink, even though nobody served them.
Sam Malone's batting statistics are implausible as it was established that the character was a career relief pitcher for the Red Sox. Relief pitchers are seldom, if ever, allowed to bat at any level of professional baseball. Also, the American League's Designated Hitter rule would have been in place prior to his major league debut.
When Nick and Carla argue in front of the bar, a crew member is visible during a wide shot of Nick.
Diane says, "I could care less" about Sam visiting an inn with a new woman. The phrase is actually, "I couldn't care less." (Being able to care less about something, as in the former version, means that the speaker does, in fact, care to a measurable extent.)