Carl Reiner asked network censors for permission to show Laura and Rob sleeping in one large bed together, reasoning (quite sensibly) that he and his wife did so in real life. The permission was denied, and the Petries are always depicted sleeping in nearby twin beds (as was the custom of TV series of the era; "Bewitched" and "The Munsters" being the exceptions to the rule).
Carl Reiner would often ask cast and crew members about funny things that had happened to them, then he would write whole episodes about these occurrences. As a result, a majority of the episodes over the course of the show's five season run were based on actual events.
The Dick Van Dyke Show (1961) was the last show to have its entire run filmed in black and white. The show was due to be shot in color after the fifth season (as the 1966-67 television season marked the mandatory color filming/taping of all network prime-time shows), but never happened because of the cast and producers' decision to end the show after five seasons.
Reportedly Mary Tyler Moore told the producers she was older than she really was in order to get the role of Laura. This fact was later incorporated in episode Laura's Little Lie (1963) in which Rob and Laura have to get re-married in Very Old Shoes, Very Old Rice (1963) because Laura had lied about her age, telling Rob she was 19. In reality, she was only a 17 year young damsel. Mary Tyler Moore was born in December 1936, which would make her 24 when the show first aired in 1961.
According to Dick Van Dyke, viewers used to make bets (during the opening credits of seasons 2, 3, 4 & 5) on whether or not Rob Petrie would stumble over the ottoman, when walking through the door of his house.