Consistently worthless items

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.

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.

I sent out a mid level dweller that I got from a lunchbox card (Stephen Jones?) who had 7 Luck i believe. Found a Mirv in the wastes within about 10 minutes of leaving the vault. Miracle indeed but proof that what you find is essentially a roll of the dice.

It's totally random, I sent a bunch of 1 level dwellers with no special skills and no stimpacks what so ever out trying to kill them off cause my vault was full. As I was checking if they are dead yet so I can remove them I saw that some of them where still alive. Reason one of them had found the MIRV, another the gauss and so on and so on...

The more you explore, the better the items. 34 hours is a very small amount of time, if you hope to get something good. Half a month is something, though...
Also note that after 30 Days, ± 15 Minutes, your Dweller will encounter a special Location, from which a Legendary item is almost guaranteed.