As a few examples - these are species widely considered noxious that are not on the list.  I have personally spent a huge amount of time and money trying to eliminate these from my small property in Tidewater.

• Ligustrum sinense (Chinese Privet)
• Ligustrum japonicum (Japanese Privet)
• Sorghum halepense (Johnsongrass)
• Hedera helix (English Ivy)

The privets in particular are incredibly aggressive, rapid growing, difficult to eradicate once established yet still sold widely.