The paste that Ethel smears all over everything in the kitchen was composed of peanut butter, mustard, and molasses.
Verna Felton, who plays the maid, also appears in Sales Resistance (1953) as a housewife Lucy meets when going door to door trying to sell a vacuum cleaner.
The [still] shot of Little Ricky 'sleeping' at the beginning was used earlier, in No Children Allowed (1953). There, it was shown after Fred put the baby down to sleep. In both cases, they used a still shot to make it look like Little Ricky was actually asleep, and not moving around.
When Lucy starts unfolding the card table, the underside is bare. In the next scene, when she has fallen asleep on the table, there are numbers written under the table by the set manager.
At 19:12 Mrs. Porter has given Lucy a pitcher of water that is empty.