I wouldn't call them vulnerable- throughout the entire war the German army inflicted more casualties than they took, on all the allied armies but the Russians especially. By first half I'm going to presume 1940 + Barbarossa. The most common answer to as to their successes is that they used their armour more effectively than the British and French, breaking through and encircling. In Russia, the 1941 Soviet army lacked effective leadership on all levels, from the purged staff officers up to Stalin's strategic blunders. However there are probably revisionists who will point to other factors.

By 1943 onwards the German war machine in general was up against superior numbers and production capacity. On top of that, Hitler's unchecked leadership undermined the Wehrmacht's effectiveness, with his obsession with not ceding ground (akin to Stalin in the wake of Barbarossa). The Italian campaign 1943-45 shows just how good the Wehrmacht were fighting a strategic withdrawal if left without much interference from Hitler, even when under-resourced. Again, there are other factors which those more qualified can point to- for example, the Wehrmacht was reliant on millions of horses throughout the war.

Source: Storm of War, Andrew Roberts

The Wehrmact only seems unstoppable as that is part of the mythos that has been developed over the years. While yes, overall the Nazis did defeat Poland in less than a month, and overran France in less than two, you have to understand that it wasn't because they were "unstoppable", it was a combination of luck, poor planning and logistics by the Allies, as well as air superiority that allowed them to win overall, but at the same time, the Germans did take heavy casualties and did lose several engagements.

Let's start with the invasion of Poland.

Firstly, the Polish anticipated that the French and British would hold up their end of the treaties of protection and begin an offensive war against Germany (which they didn't). The entire Polish defensive plan was based around this. While some fighting did occur between France and Germany, Germany was still able to project most of its armored forces into Poland.

During the Polish invasion, the Battle of the Bzura, a Polish counterattack actually pushed the Germans back several kilometers with heavy losses. The attack proved so successful, the Germans had to redirect a German division away from the push on Warsaw to counter the attack. Additionally, German air superiority limited Polish daytime movements, which slowed their advances and clearly helped them regain the tempo. Now mind you, this armored division had suffered severe casualties including almost half of its tanks. In fact, the initial attempt to overrun Warsaw failed, which resulted in a siege having to take place, which lasted til almost the very end of the actual Battle of Poland. The only reason they capitulated was for humanitarian reasons and the civilian population. Returning the Battle of the Bzura, it was largely German air superiority that allowed them to win by destroying the necessary bridges and the Polish anti-aircraft batteries running out of ammunition.

Finally, in the case of Poland, the Soviet invasion was a total surprise and a complete violation of their treaties. This of course split Polish defenses causing them to abandon their initial defense plans.

Coming the the invasion of the Low countries and France in 1940, the Germans still were not totally unstoppable.

The German assault on the Hague was a dismal failure and the Dutch overran and captured thousands of German paratroopers. This battle also resulted in heavy losses for the Luftwaffe's transport capacity. Several attempts by the Germans to capture necessary bridges intact were also major failures. Several Dutch attempts to counterattack and recross rivers were often initially successful, but failed due to poor exploitation or German counter-attack. Overall, the Dutch army was able to retreat largely intact and maintain a relatively strong defensive line. What ultimately led to the Dutch surrender, despite being cut off from it's allies, was threats of heavy German bombing like what had occurred at Rotterdam and Warsaw.

During the Battle of Hannut, French and Belgian forces fought a strong delaying action against German forces and inflicted extremely heavy casualties on the Germans.

At the Battle of Gembloux, the French repeatedly held off German attacks, but could not sustain the losses ultimately (though it did allow the British and French to evacuate to England).

While the French did lose the Battle of Arras, their counter-attack was strong enough to give the Germans pause and allow the British and French to withdraw.

The German invasion of Crete was ultimately a victory but was so costly and botched, the Germans never launched another major airborne operation again.

Overall, the key to German success in 1939 and 1940 was the superiority of the Luftwaffe, not the Heer (army). Repeatedly Polish, Dutch, Belgian, French, and British forces successfully counter-attacked, held strong on defense, or even overran German forces, but were repeatedly defeated due to air superiority, heavy attrition, or a planning or logistical failure.

I've only skimmed the surface, but the myth of the unstoppable German army of the early war, is just that, a myth. Certainly the Germans were a fantastic war machine, utilizing new technologies and tactics that allowed them major tactical advantage, however, the overall quality of soldier, ability, and morale, was not much beyond their opponents.