Consistently worthless items

Solution 1:

The quality of items you find is directly tied to the length of time the dweller is out in the wasteland. Their survivability of course is related to their level (health) and the number of stims/radaways you give them.

Basically just wait longer. The longer they are out there, the better chance of getting a better drop. There are no guarantees of course, but if they can survive out there for several more days, leave them for as long as you can and you should get better drops. Since they take no damage or radiation while on their way back, you can wait until they are literally 1 hp away from death before recalling them to get maximum exploration time.

Solution 2:

A person here:

https://www.reddit.com/r/foshelter/comments/3awycu/chance_at_a_legendary_comes_just_after_hour_60/

says that after hour 60 you get a chance of getting legendary item, then you might or might not succeed opening the crate with the item.

Here is what he says:

I got my first two legendary items from the Wasteland today. Appears that the event is set to occur shortly after 2 and half days out from the vault. While it appears the event will always occur - based on the four screenshots below - success isn't guaranteed. If I had to guess, it is probably based on Agility - Lockpicking is based on Agility if I recall - but I'll have to take a closer look at the stats of the two people who succeeded.

National Guard Depot - Success 1 [1]
National Guard Depot - Success 2 [2]
National Guard Depot - Failure 1 [3]
National Guard Depot - Failure 2 [4]

This is not to say that this is the only chance at a Legendary. This is just the only one I've managed to identify so far. I got lucky by having two of them drop so close together and being able to capture the logs. That they both occurred so soon after the 60 hour mark led me to watch for the event in my other two explorers who were approaching that mark.

Now that I know that an event can be associated with a specific time, there are a few other events I've identified associated with Rare drops that I can check to see if they occur with some regularity.