One of the unusual things about Richard II (coming Friday!) is that it's written completely in verse. In particular, it's in iambic pentameter (10 syllables to a line, with every other syllable stressed), and there are often rhyming couplets (two lines in a row that rhyme). Usually in Shakespeare, characters from the lower classes speak in prose, but in Richard II even the gardener speaks in verse. The only other Shakespearean play like this is King John. Not being an expert on Shakespeare myself, I got this information from the excellent Old Vic Theatre's Educational Pack on Richard II.
According to ShakespeareNYC, Richard II was written at the same time as Romeo and Juliet and A Midsummer Night's Dream. The ShakespeareNYC web site also credits Richard II (the real king) with the invention of the handkerchief. For more info on that, check out this site.
Your last fun fact of the day has to do with John of Gaunt. According to Shakespeare Online, Holinshed's Chronicles (the history that Shakespeare used as a source) portrayed him as a "disorderly and rapacious magnate". Shakespeare's queen, Elizabeth, traced her lineage directly to John of Gaunt, which is one of the reasons why Gaunt became a wise and noble patriot in the play.