Robert has put together a timeline for events occurring before Muster, set in April 1594. These events are from 1593, as nothing of import seems to have occurred until May of 1594.
Given the speed which information passed in period, all of the events would be known to the citizens of London by Muster. You may have even seen the various plays listed, as well as others from previous years. Here are some starter links if you wish to research any of these for more details for gossip to spread at the event.
January – John Norden commissioned to make maps of all the counties of England. Speculum Britanniae: the First Parte: an Historicall, & Chorographicall Discription of Middlesex was published later this year.
February – London’s theatres were closed again due to an outbreak of the plague, and many players left the capital to tour the provinces. No theater performances since then.
23 February – Peter Wentworth imprisoned for raising the issue of succession to the throne in Parliament.
6 April — Henry Barrow and John Greenwood, puritan Separatists, were hanged at Tyburn.
– The Witches of Warboys, Alice, John and Agnes Samuel, having been found guilty of witchcraft, were hanged at Huntingdon.
5 May – “Dutch church libel“: Bills posted in London, on the wall of a Dutch churchyard in Broad Street, threatening Protestant refugees from France and the Netherlands allude to Christopher Marlowe’s plays.
12 May – Arrest of dramatist Thomas Kyd in connection with the “Dutch church libel”. “Atheist” literature found in his home is claimed to be Marlowe’s.
18 May – A warrant for the arrest of Christopher Marlowe is issued. On 20 May he presents himself to the Privy Council. A theory on the framing of Marlowe
29 May – Execution of the Welsh Protestant John Penry suspected of involvement with the Marprelate Controversy.
May 30 — Dramatist Christopher Marlowe is stabbed to death in a dispute over the bill at a lodging house in Deptford.
September — Irish pirate queen Grace O’Malley meets with Queen Elizabeth at Greenwich.
Publication of Shakespeare’s poem Venus and Adonis.