Bernard Cornwell, author of the Richard Sharpe novels on which the TV series was based, was so happy with Sean Bean's portrayal of his hero that he changed the physical description of Sharpe in his later books to more closely resemble the actor.
Sharpe's 95th Regiment and its green jackets are fact based. The 95th was a direct ancestor of the modern Royal Green Jackets (in 2005 merged with other regiments to form The Rifles).
The jacket which Sean Bean wears on the cover picture was actually tailored for the smaller Paul McGann, whom Bean replaced in the role of Sharpe, which is why the jacket hangs open at the front.
In one scene, Vivar is seen to light a cigar with what appears to be a pistol with no barrel. This is, in fact, a flintlock fire-starter - pretty much exactly a pistol grip and lock with no barrel, designed to ignite tinder by means of the shower of sparks created when the flint in the lock strikes the steel frizzen.
The "proper sword" given Sharpe by Capt. Murray is a the British Pattern 1796 Sword for Heavy Cavalry. It is a single-edged sword with a "hatchet" point similar to that of the Japanese katana. Also like the katana, the 1796 is meant to be a cutting sword, though this blade-heavy weapon is meant for much less elegant work than the well-balanced katana. As such, the 1796 is particularly unsuitable for delicate swordplay; nonetheless it found strong favor among British foot as well as horse troops especially during the Napoleonic Wars due its ability to simply break the blades of lighter infantry and cavalry swords - allowing users to smash their way through opponents.