Born and raised in Sweden I can definitely see some challenging differences. The Swedish sense of humor is one big challenge. Another is the way in which Americans engage in small talk. Swedes tend to be more to the point.
And you are so right about the let’s-get-together phrase that usually doesn’t mean much to Americans. Americans are more willing to move for work and when they move it is often far away. They can quickly attach themselves to new groups etc. Friendships are usually less permanent. And less is expected from an American friendship than from a Swedish one.
Check out my article on the Swedish expression Lagom if you get a chance — another take on American-Swedish cultural differences.