This review will only really deal with the routes as they are, and using Mapnik. If OSM's road names are wrong, or the roadways off, then I won't be addressing those issues. If there's incorrect routings on TM that match OSM then I won't spot them. I might find something in GMSV (such as TN7 Truck)
TN1 (Memphis): point required (grade-separated junction) at North Watkins Street. You probably want at least another point - I'd suggest McLean Blvd
TN1 (Sparta): good
TN2: good
TN3: point required (intersecting route) for I-40 exit 1A. CheAve -> 2ndSt_N ? point for Jefferson Avenue?
TN5: TN21 -> TN21_E
TN7 (Columbia): Those odd junctions probably ought to have point on the link road, rather than the overbridge. Point at North James Campbell Blvd?
TN7 (Ardmore): The state line is signed as being the railroad. At the AL53 junction
TN7 is signed straight on along Main Street, but other than the TN7 Truck Route sign (see below), there's nothing else beyond referring to TN7. I'd leave things as-is.
TN7 Trunk (Ardmore): New Route - While looking to see whether AL53 was genuinely at the border, I found a sign for a truck route of TN7 - it goes
Ardmore Ridge Road,
Austin Whitt Road and
Austin Street.
TN8 (McMinnville): could have side roads rather than hidden points, but you've discussed that.
TN8 (Chattanooga): good
TN10: could have side roads rather than hidden points, but you've discussed that.
TN11: good
TN12: TN49 points - make reference to TN249 as well?
TN13: good
TN14: add points for GSJs with Old Austin Peay Highway (x2) and Scott Street. Add points added to TN3. Think about adding more points to route along Jackson Avenue.
TN15: good
TN16: good
TN17: points at Central Avenue and Holtzclaw Avenue (link to nearby freeway exits), ditto on US41 and US76. point at either Bailey Ave or McCallie Ave for route towards US11/64
TN18: good
TN19: good