Definitely one of those early twentieth century murder mystery / dinner theater clichés, a blunt instrument is any non-projectile weapon that doesn't have a blade. Candle holders, ornamental clocks, clubs and maces are all blunt instruments.
Colloquially, blunt instrument is a term used to describe any sweeping use of force or authority - school officials banning all internet access to prevent the spread of viruses can be described as the officials wielding a blunt instrument.
The phrase is rarely seen on its own in this context - it almost always is meant specifically to reflect back on the user of such authority and is always meant pejoratively - The major problem with using such a tool is its habit of taking out quite a few innocents in the process.
Similarly, an artist (be they a writer, a lyricist, a filmmaker or what-have-you) utilizing extremely obvious metaphor to clumsily prove a point is said to be wielding a blunt instrument.