What was the most stupid thing the League of Nations had done? We can choose the failure of the League in Manchurian crisis and Abyssinia crisis, because these became important cause of World War II. Thus, these two things were also very huge affairs in history.
Manchurian crisis happened in 1931 through invasion of japan to Manchuria. (The cause of this crisis was desire of Japan to build on empire.) And this crisis results terrible things to the League.
At first, everyone was ashamed of the League and the League scared no one.
League couldn't do anything about this crisis. When Japan kicked out the chinese and set up their own government, China asked for help to the League of Nations.
At that time, what the League did is just sending a group of officials. Guess what? It even took a year before the League decided to condemn Japan! and League ordered Japan out of Manchuria, but Japan refused to accept it.
Instead, japan left the League in 1933 because Japan knew the League doesn't have real power.
The League should punish Japan through something. So it made sanctions to Japan. But It was useless because other countries didn't want to quit their trade with Japan. In fact, they couldn't even stop weapons trade with Japan. (Since at that time, countries went bankrupt through The Wall St Crash, those wanted to increase their own wealth.)
So at the result of that, the League showed only its weakness to Japan and whole world. (Nobody scared the League anymore and everyone thought the League was shame because of Manchurian crisis)
The second, Japan became extremely proud of the army.
At first, when Japan was in the League it received limitation on their army by the League of Nations, and couldn't act freely. But through this affair, Japan could enhance their army without interruption of League and thought the League was loser which couldn't do anything to Japan. In addition to that point, Japan have proud of the its army because it's army became strong and any country couldn't ignore Japan anymore. So Japan would have plan to enhance its army more and more. And the result became World War II
Abyssinia crisis which happened in 1935-1936 was done by Italy. (Mussolini)
This crisis also results terrible things to the league.
At first, The league was no longer trusted again.
When Italy invaded Ethiopia, Ethiopia emperor Haile Selassive went to the League to ask for help. At that time, what the Britain and France(Main member of the League of Nations) did was to sign Hoare which means giving Ethiopia to Italy!
It was really fatal thing to the League. Any countries which were in the League of Nations couldn't trust the League anymore and did their own way to increase their own wealth.
The second, it showed how the League was incapability.
When the Italy intended to invade Ethiopia, the League talked to Mussolini to persuade not to invade Ethiopia. But when they were talking, Mussolini sent his army to Ethiopia. So the League became a fool.
It is same that when Ethiopia emperor asked for help to the League, the League secretly sighed the Hoare which means giving Ethiopia to Italy.
It was awful! Italy which knew the League was nothing, conquered Abyssinia and left the League in 1937. and the League was also never trusted again.
The third, it became chance of German which wanted to conquer other lands.
While the League was distracted by the Abyssinia crisis, Hitler who became German's boss marched 22,000 soldiers into Rhineland.
If you compare those two crisis, both of those gave fatal damage to the League. But as you know, Abyssinia crisis was more direct cause of World War II compared with Manchurian, because it gave chance to Hitler for invading Rhineland. Therefore, I think Abyssinia is more terrible affair to the League. But it's true that both Abyssinia and Manchurian were very important affair to the League (bad effect)