My suggestion would be to have weekly challenges be things that are on top of normal missions. So for example you might have to set up a Sat-dish or take water samples during a mission where those things don’t already occur. Shoot skinned bodies down from trees and collect dog tags.
New Equipment/Gear could also play a part.
A camera that has a weight of one but allows for photographs to be taken. Points are awarded for each enemy type, installation or train wreck.
USB keys that need to be added to computers on the map, these things can take up a gear slot or just be doable when that weekly mission comes up.
Scavenger Hunt Weekly
The other idea is to have a scavenger hunt, each time this mission comes up a set number of items will be added to the map, say about 20. Each mission you’ll possibly find some and when you find them all you complete the challenge, this is done over a number of games not all at once.
It could also be fun for the community to try and identify what the items are by keeping them secret but giving us a blank list with the number of letters in each item. Like hangman ie. _ _ _. These could have Easter eggs relating to the movies or resized and repurposed assets.
Items can be hidden in the breakable wood crates.