The Battle of New Orleans actually occurred after the end of the War of 1812. The Treaty of Ghent was signed on December 24, 1814. The battle took place two weeks later.
The British 7th Regiment was never part of the British order of battle that faught at the Battle of New Orleans, however, the Scottish troops depicted were the 93rd Highlanders and they did fight, taking frightful casualties.
It is interesting the reference to Brigadier General. While wearing the correct insignia, Southerland should be referred to as simply 'Brigadier. The British Army eliminated the rank of Brigadier General in 1921, replacing it with 'Brigadier' a few years later. Note that the British do not refer to Brigadiers as a Generals Officer. The American Army still has Brigadier Generals.
When Gen. Southall is transferred back to 1815, he is shown moving through the time vortex. Throughout the run of the series, more than a dozen characters are transferred by the Tunnel, but this is the only time that anyone other than Tony and Doug is shown in the vortex. The others just disappear from one time and appear in another. Southall is the only traveler to land his feet in the course of the entire series. Our heroes always fall and tumble when they arrive for their next adventure
This episode takes place near New Orleans, Louisiana from January 6 to January 7, 1815 and in Arizona in 1968.