The most frequent problems arise when a Special Forces team, which often includes several members who speak the local language (usually Arabic), bump into an army or marine officer (usually a battalion or brigade commander) who has ideas that conflict with those of the Special Forces guys. Despite the fact that everyone has been told to work these things out, and that any "unfortunate" (ending up in the media) incidents resulting from these feuds would hurt career prospects, collisions occur anyway.
The basic problem is that most Americans have to deal with Iraqis through interpreters, while the Special Forces troops, who all speak several languages, often have one or more of their people who speak the language and are able to establish personal relationships with local Iraqi leaders. This is the sort of thing the Special Forces train for and specialize in. Even though the Special Forces also know, from decades of experience, that they have to make sure the local army or marine commanders know what is going on, the Special Forces methods look, well, odd, to a conventional military mind. While the Special Forces have exceptional military skills, their appearance is often off-putting to regular troops. Special Forces in places like Iraq will often grow their hair a bit longer, and sometimes on their face, in order to better fit in with the Iraqis they are schmoozing.
Despite over half a century of efforts to eliminate these culture clashes, they still occur. And it still becomes a problem when the Special Forces and regular military cannot agree on how to deal with a situation, and neither has any authority over the other.
In Iraq and Afghanistan, commanders down to battalion, and sometimes company, level, have been given a lot of freedom to use their initiative in dealing with problems they encounter. That's great, but it does cause some problems when there are several U.S. entities (military, Special Forces, civil affairs, NGO, State Department, and so on) operating in the same area. Typically, no one is in overall charge. This is a particular problem when the action unfolds in a location that is heavily influenced by tribal leaders. Outside of the cities, there are many locales where members of individual tribes are concentrated enough so that the tribal leadership is, for all practical purposes, the local government.