Mussolini's greatest mistakes were those decisions he took without consulting Hitler.

The Italian entrance into ww2 happened as France was falling. Mussolini was convinced that the war would be over within a few weeks and that some Italian particpation was necessary to secure Italy a place at the negotiation table (and spoils).

The Italian 1. and 4. Armies of some 32 divisions (although Italian divisions were smaller than other nations' divisions) could make no headway against the French Army of the Alps of some 6 divisions (entrenched in the Alps and protected by extensive fortifications).

Worse for the Italians was that the British refused to surrender and kept fighting, which meant that more than a third of the Italian merchant navy (much of it important and rare tankers) was caught outside the Mediterranean and sunk or captured by the British. The Italians had 786 ships (of 500 tons or more), for a total of 3 318 129 tons, and about 200 ships (of 100 to 500 tons). As many as 212 ships, amounting to 1 216 637 tons, were lost due to the rash decision to declare war.

As the Italians needed all merchant ships they could get - not only for their own coastal trade, but also to supply Sardinia, Sicily, Albania and Libya as well as Rhodes and the Dodecanese Islands.

Had Mussolini waited, his merchant fleet could have been ordered home, carrying much needed rare materials, oil and coal, which would have improved the Italian industrial situation and helped with the Italian fleets cronic shortage of fuel.

The decision to declare war also left Italian East Africa stranded - the British controlled both the Suez Canal and Gibraltar, and there was no way to bring reinforcements or supplies to the Italian garrisons of Ethiopia, Eritrea and Somalia.

Then Mussolini ordered the 10. Army to attack British Egypt from Italian Libya. The 10. Army consisted almost completely of foot-marching infantry with scarce supplies of AT and AA guns only around 90 weak tanks (M11/39) and about 200 tankettes (only armed with machineguns). The artillery was mostly vintage ww1 pieces and few in numbers, even if the Italian artillerymen were exceptionally brave and well trained (they would on several occasions remain to fire directly at British tanks rather than retreat). The Italians advanced some 100km to Mersa Matruh, and then stopped, needing to secure their supply lines and bring forward water, food, ammunition and fuel. They dug into several fortified camps.

The British took the time to send substantial reinforcements to Egypt, including all of the 7. Armoured Division and parts of the 7. Royal Tank Regiment, equipped with heavy Matilda Mk II tanks - with armour so thick no weapon in Africa could knock it out. The resulting campaign destroyed 10. and 5. Army (the latter originally stationed in western Libya) and the reinforcements sent in an attempt to shore up the situation - causing the Italians to lose about 250 000 men dead, wounded or prisoner, several hundred artillery pieces, some 200 tanks (M11/39 and M13/40) and 200 tankettes.

After this devastating defeat, the Italians had to ask the Germans for help, which came in form of Rommel and his famous DAK (Deutsche Afrika Korps).

Another huge mistake Mussolini made was to invade Greece.

Mussolini saw himself as an equal partner in the Germano-Italian Alliance, but the Germans did not see it the same way. The Balkans, which had been united in the Little Entente Alliance (Yugoslavia, Romania and Greece) to keep the losers of ww1 (Austria, Hungary and Bulgaria) in check, under French influence, was ripe for a new master. Mussolini fancied himself as a new puppetmaster of the Balkans, but the Germans moved into Romania Autumn 1940 - without informing the Italians beforehand. Mussolini, feeling slighted, decided that invading Greece in October 1940.

As the Italians were sitting at Mersa Matruh in Egypt, waiting for reinforcements, supplies, fuel, artillery tanks and trucks, all of that went to the Italian army in Albania.

Attacking the Greek mountains in winter was not a good idea, and the Italians were woefully unprepared for the weather, while the Greeks fougth valiantly. The Greeks stopped the Italians and then drove them back in a flanking offensive that saw the Italian line collapse and the Greeks occupy the southern third of Albania.

These three decisions (and two campaigns) pretty much crippled the Italian ability to wage war independently, and any campaign they undertook afterwards were under German command with the brunt of the work done by German forces.

So, three bad decisions and two disastrous campaigns undid Italy rather than an inability to understand German, as the Germans were in no way involved in any of these three.

Edit: Spelling.

Follow-up : I've heard that Franco didn't join Hitler in the war because of poor translators. Is it true ?

Absolutely not true!

Mussolini spoke fluent German and there is film of him speaking to German audiences. For example, his 1937 speech in Berlin. He was able to speak with Ribbentrop, Hitler, and other German officials without the aid of a translator.

He also spoke passable French and pretty good English.