Some problems alien races have are differences of opinion between close worlds and on their own worlds.
One party may want to do something one way and another party may want to do something another way.
Misunderstandings happen all of the time wherever you have a diversity of life.
The largest differences between primitive life (like us) and advanced life are in "how" they prevent and solve their differences.
Advanced life has had much more time for experience, and also share knowledge and abilities to help one another.
Third Parties
Advanced races regularly use mediation by independent third party.
They choose someone who is highly respected by all sides, or they already have such a person in place.
Each party who has the disagreement may want something different, but they each want the same one thing the most, which is peace.
Nobody always gets everything he wants.
Everyone helps to just get themselves and everyone else as close to what they each need as possible.
Example
For instance, if a number of races use a resource from a world, and one of those races begins to need more and this becomes a concern to the others that their resource will become depleted, this would be a problem.
Mediators
Some races are especially widely known and respected for their natural abilities of personality and wisdom.
These races are usually among the most advanced in an area, and many particularly skilled members of such a race may be employed in a group of worlds as mediators.
Conclusions
Other kinds of problems advanced races have are similar to ours, such as disease and limited technologies to achieve the next particular obstacle.
But again these problems have been and are handled in advanced ways, so they are much less occurring and less lasting.
