A Brief History of Washington County, Virginia explains1 why there is a "notch" in the Virginia - Tennessee border:
The southern boundary line of Virginia was assigned to parallel 36°30'. In 1749 when Peter Jefferson, father of Thomas Jefferson, surveyed from about where Patrick County is today, he kept moving farther north away from the assigned parallel till he discontinued his survey east of Damascus. In 1800, the northeast tip of the new state of Tennessee joined Virginia and North Carolina on Pond Mountain. Tennessee continues on that northern parallel in Washington County, until it jogs south but not to 36°30'. Three stories are told about the Notch: (1) the surveyor was inebriated (2) iron deposits in the Iron Mountains interfered with readings of the compass and (3) the strong will of Tennesseans prevailed.
1. A Brief History of Washington County, Virginia, Count of Washington, Virginia Government Information, www.washcova.com/resources/history.php (last checked October 23, 2004)