I’ve found an interesting link about how to retrieve some properties of user profiles in SharePoint 2013 by using its client object model, like this:

const string serverUrl = "http://serverName/";
const string targetUser = "domainName\userName";
ClientContext clientContext = new ClientContext(serverUrl);
PeopleManager peopleManager = new PeopleManager(clientContext);
string[] profilePropertyNames = new string[] { "PreferredName", "Department", "Title" };
UserProfilePropertiesForUser profilePropertiesForUser =
     new UserProfilePropertiesForUser(clientContext, targetUser,
     profilePropertyNames);
IEnumerable<string> profilePropertyValues =
     peopleManager.GetUserProfilePropertiesFor(profilePropertiesForUser);
clientContext.Load(profilePropertiesForUser);
clientContext.ExecuteQuery();
foreach (var value in profilePropertyValues)
{
     Console.Write(value + "n");
}
Console.ReadKey(false);

You can find more information in:
http://msdn.microsoft.com/es-es/library/jj163182(v=office.15).aspx