Help identifying pests or diseases affecting young melon plants
We are not concerned by what we see in your photos.
The plants are young and it's early in the season and they should easily grow out of what looks like minor damage from occasional feeder damage, and perhaps our unusually wet weather.
The insect looks like a planthopper, which is not of great concern. (They are not easy to catch on camera!)
We suggest giving the plants a shot of soluble fertilizer.
You could also consider using a floating row cover to limit insect access. (Here is our page about that: http://extension.umd.edu/hgic/floating-row-cover )
Time is on your side. There is plenty of time to replant if things don't go well from here on out. Given the longer season for melon, we'd suggest replanting with transplants that are more sturdy from the get-go.
Here is our plant profile page for melon which includes the many common problems they can have: http://extension.umd.edu/hgic/learn/cantaloupe