I know not why Shakespeare calls this play a Midsummer-Night's Dream, when he so carefully informs us that it happened on the night preceding May day. (Johnson 1908:71)
Samuel Johnson's note to VI i 103 (the line number is adjusted to correctpond with the Arden edition) has been reiterated by several critics. Both Mayday and Midsummer Night share associations with magic and the supernatural. Ernest Schanzer points out that there are certain qualities which are thought only to belong to Midsummer and not to Mayday:
But there are three associations which the eve of Mayday did not share with Midsummer Night: that of flower magic, the notion being that certain herbs and flowers gathered on that night possessed various wonder-working powers; that of lover's dreams; and that of madness. (Schanzer 1965: 26)
Schanzer sees "love-madness" as the central theme of A Midsummer Night's Dream, and therefore finds the last association the most important.
Alan Bellringer argues that an important theme in the play is the relationship between the human and the non-human. "The fairy world most felicitously represents that non-human power which it is common at once to fear, to warm to, and somewhat to despise," he writes:
The shortest night of the year, when the earth begins to tilt the nothern hemisphere back towards winter, is a date highly charged with significance, reminding us of the patterned change in physical nature on which we depend for life. The folk-customs associated with the shortest night can be felt to assert humanity in the face of forces beyond human control which nevertheless, miraculously, afford us the conditions for life. Enchantment is a primary literary metaphor for this sense of lucky dependence. (Bellringer 1983: 201)
Perhaps it makes no difference which day the play's events are supposed to take place. C. L. Barber argues that May Day need not necessarily be the first of May. "People went Maying at different times. (..) The point of the allusions is not the date, but the kind of holiday occasion." (Barber 1959: 120).