Other than trouble with the Muslim population and a World War, I don't think there were any major problems. The Muslims also fought against the Spanish, the Japanese and the Philippine government.
It wasn't just the Muslims in the Philippines. That came later. A change in administrations back home didn't help, but we can hardly blame General Aguinaldo for feeling betrayed when comments like Admiral Dewey's statement that the US "had come to . . . free the Filipinos from the yoke of Spain." were followed up eventually by a U.S. general assuring Congress that Filipinos who wanted freedom had "no more idea of its meaning than a shepherd dog."
To quote one good selection from Katz at NYU:
President McKinley said he spent many sleepless nights agonizing about the Philippines. The president called his program "benevolent assimilation." The influential San Francisco Argonaut was more candid: "We do not want the Filipinos. We want the Philippines. The islands are enormously rich, but unfortunately, they are infested with Filipinos."
A U.S. army of 70,000 [including 6,000 Black troops] was sent to pacify the islands and, as more than one white soldier said, "just itching to get at the niggers." General William Shafter told a journalist it might be necessary to kill half the population to bring "perfect justice" to the other half.
After General Jack Smith promised to turn the Philippines into a "howling wilderness" most casualties were civilians. Smith defined the foe as any male or female "ten years and up," and told his soldiers: "I want no prisoners. I wish you to kill and burn; the more you kill and burn the better it will please me."
These guys were not representative of the initial American intervention, but the fact is that it started off well and quickly got less well-intentioned than most of America's interventions. Their decisions once victoriuous came nowhere close to even paying lip service to their stated aims. My sympathies are with the Filipinos on that one.
Looking onwards however, I think the US have done an excellent job of rebuilding links and bonds since the Marcos years. The Phgillippines are a flawed, weak country and it's good that the bitterness of previous periods isn't there between the US and either the govt. or civilian population (Muslim rebels obviously excluded!).