|What should I do about the brown, twisting "roads" that are appearing on the leaves of all my tomato plants?|
|Those are leaf miner tunnels. A tiny fly-like insect lays an egg in the leaf. The egg hatches into a tiny larva that feeds between the upper and lower surfaces of the leaf making those squiggly lines you are seeing. Then the larva drops to the soil to pupate and return as an adult.
Insecticide sprays won't affect the larvae, since they are hidden inside the leaf. So the only "control" is to repeatedly spray the foliage to try to kill the adults. This requires lots of spraying and is just not necessary since the damage these insects do is usually not severe enough to warrant control. The secondary damage to beneficial insects caused by pesticides usually outweighs any benefits.
This "minor miner" damage shouldn't affect your crop.