My understanding is that George Washington was a mediocre general, with many of his support staff being equally untalented. Especially in the early years of the revolution the continental army was beset by losses, even in situations where more canny tactical decisions may have resulted in victories.
Further down the road it seems abundantly clear that the US civil war lasted as long as it did in large part due to the ineptitude of Union high command. McClellan was over-cautious and refused to pursue the enemy without overwhelming numerical superiority. Hooker was rash and overly impulsive. Even Grant, if I recall correctly, relied primarily on his massive superiority in numbers and munitions, taking disproportionately heavy losses in combat.
Throughout the 19th century military planners and logicians made serious blunders as well. During the civil war Union officials notoriously rejected the idea of arming soldiers with breach-loading or repeating rifles in favor of rifled muskets in fears that soldiers would waste ammunition. Later, during the Spanish-American war American units were armed with Krag-Jorgenson rifles which were far outclassed by Spanish Mausers. Likewise I have read that US forces continued to employ Gatling guns over early machine guns, despite their greater weight and lower rate of fire/poorer accuracy.
After America's entry into the first World War US officers insisted on using frontal assaults long abandoned by the French and British, despite repeated warnings by their allies that these tactics wouldn't work.
Finally, during World War II I've read that German soldiers criticized their American counterparts, claiming that American units rarely used properly coordinated attacks with infantry and armor, and that their military success seemed more rooted in the fact that they had nearly unlimited quantities of all resources.
I recognize that the United States' immense population, industrial capacity, and resource base has long served as its greatest military asset. That said, is it fair to say that (maybe as a result?) there is a history of poor leadership and tactical thinking?
I can speak to the earlier portion of your question (19th century), and will let other historians specializing in 20th century American history take over from there. For starters, though, I think you have to throw out the American Revolution for the purposes of this discussion, since the country as it is known today was still in the process of being formed. George Washington was born in Virginia, yes, but was a trained British officer for the entire portion of his life leading up to the Revolution. Many of the other officers on the colonial side had various European backgrounds (von Steuben, for example). If you want to extend that consideration for the War of 1812 (which, admittedly, didn't showcase dazzling American generaliship) and start with the Mexican-American War, I think that would be a fair starting point.
The Mexican-American war absolutely DID showcase some exemplary military leadership in the form of Winfield Scott and Zachary Taylor, not to mention a veritable all-star line-up of up and coming young officers that would make names for themselves in the American Civil War (ACW). The American military went into foreign territory, and proved that its military was more than up to the task (the leadership and young officer corps included).
And in the ACW, these young officers proved that their American military training (West Point, VMI, etc.) and battlefield expertise (Mexican American War) was currency that spent well in a massive, game-changing conflict that had a dramatic impact on the arts of warfare the world over. Although there were some very bad generals in the ACW, there were also some fantastic ones. Robert E. Lee was an unquestioned military genius who was as good on the offensive as he was on the defensive. A human being that was prone to mistakes, sure, but Lee was the equal of any general alive at the time. Grant, far from the laboring butcher who relied solely on numerical superiority, was a tenacious, creative, and flexible general who actually found success most often when he maneuvered and worked to get around the flank of his opponent. While he initiated a number of brutal frontal assaults during the Wilderness Campaign (Cold Harbor, Spotsylvania Courthouse), this was usually only done after he'd attempted to outmaneuver Lee and get between the Confederate general and Richmond. Modern military assessment holds Grant in a much higher regard than you give him credit for. Likewise, Gen. Longstreet, Gen. Sherman, Gen. Stonewall Jackson: all are legends. Now, don't get me wrong: all were human beings, too, and like all generals, they made their fair share of mistakes (Jackson during the Seven Days, for example). Even McClellan, while a lousy battlefield commander, was a great organizer and trainer, and even though he didn't know how to effectively use his troops, most agree that he did a damn fine job getting the largely civilian rabble into fine fighting shape. The Navy of this time likewise produced a number of outstanding admirals (Farragut, Dixon Porter, Foote).
All of these men were American born. And while I'm not saying that they were necessarily "better" than their contemporary European counterparts, I think they deserve respect as outstanding examples of fine American military leadership. So to answer your question, at least as it concerns 19th century American military leadership: no, I don't think you can make a convincing case that Americans were lacking compared to other nations.
[Note: nothing is cited in this response since nothing stated is a direct pull from any specific resource. To read up on American military leadership during the ACW and to some extent, the Mexican American War as it relates to ACW leadership, Bruce Catton's Army of the Potomac trilogy is a great place to start. Doris Kearns Goodwin's 'Team of Rivals' gives readers an excellent look at the politics underpinning military leadership during the ACW. Jay Winik also has a great distillation of this topic in 'April, 1865']