This guy is fantastic.
It's a long video, so here's a brief synopsis: Most of the arguments against free immigration are based on claims that are at best exaggerated. Moreover, even if we accept all of the reasons usually given, there are cheaper and more humane ways to deal with the problems mentioned. For instance, if we're concerned about immigration lowering wages (which doesn't happen to any significant extent) or about immigrants soaking up welfare benefits (which really aren't that much to begin with) there is a simple solution: charge a flat fee for immigration (say, $30,000), or have a higher rate of taxes (say, an extra 10%) on immigrant workers. These suggestions are just concessions, of course. The real point is this: once a reasonable person has heard the facts, there really is no moral reason why he should oppose open immigration.