It certainly had an effect, but not a particularly huge one.

The worst offender which comes to mind is that of the US Navy's submarine torpedoes, which had a nasty habit of failing to go 'boom' when they were at the target. The US Navy's website covers the failures of both the German and US torpedoes in this rather informative two-page article.

http://www.public.navy.mil/subfor/underseawarfaremagazine/issues/archives/issue_47/torpedo.html

In the realm of artillery ammunition, the really big one was the development of the VT fuze. This was a fuze fitted with a tiny little radar which determined how far above the ground the shell was. This resulted in the round bursting an ideal altitude above the ground, causing lots of fragmentation over a wide area, with devastating effects. It was not used until the very end of 1944, however, so was not something upon which the war hinged. Similar fuzes could be found in the anti-air role, though given the US air superiority by this time, its practical effect was, again, limited. I am unsure about its prevalence in the Pacific in 1945, perhaps someone else can chime in on it.

In terms of tank ammunition, the US had some issues, being unfamiliar with the use of large calibre ammunition against tanks. The original M72 AP ammuntion fired from the M3's 75mm gun had terrible performance against the German armor, to the extent that the British started mating captured 75mm projectiles with the US's cartridges. This was fixed relatively quickly with the M61.

Similarly, the US for whatever reason failed to develop a suitable HVAP (High Velocity Armor Piercing) round until after the desperate call went out in July 1944 when it was discovered that the 76mm and 3" guns were not quite as effective against German tanks as expected (The reasoning was that the tungsten required was better used in other parts of the war effort, but I don't see why that should have stopped development). Although a crash construction program fielded the ammunition within two months, there was never enough to go around.

It's not that the Germans were absent their own problems. The squeeze-bore guns were reduced in distribution because of their own issues with tungsten supply, for example.