1-4 days after having sex with Lady D'Arcy, Macleane complains of having "the pox" (syphilis) and that his genitals are a "disaster area". This is impossible - syphilis symptoms take at least a week to develop and are initially (for the first few weeks) painless and very minor. However, given that medical science and knowledge were fairly rudimentary in the 18th century, it could be that Macleane had picked up a different STD and was getting it confused with syphilis. But even then, STDs do not generally show noticeable symptoms within such a short time of exposure.
While there was an Earl of Rochester extant in 1748, he would have been 76 years old, and was certainly not known as a bisexual profligate. The character seems to be based upon John Wilmot, 2nd Earl of Rochester who lived during the reign of Charles II and died in 1680.
When Plunkett is teaching Macleane how to shoot, Macleane accidentally fires his pistol and kills a pheasant. If they had just been discharging firearms (at least twelve times, according to the score), there would most likely not be any pheasants within half a mile, nevermind pistol range.