Acts 10:34Then Peter began to speak: "I now realize how true it is that God does not show favoritism 35but accepts men from every nation who fear him and do what is right.
Does this favor the argument that “the world” and “all” in other passages means people from every nation?
Or, does this favor the argument that Peter, who has just had to be whapped upside the head for limiting his understanding of the grace of God toward salvation, has now learned better–but may still be not understanding (or accepting?) the full extent of the grace?
(Hint: does Peter ever have to be whapped upside the head again for limiting his understanding of the grace of God toward salvation? I seem to recall that he does… 
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It does seem to contradict verse 28:But God has shown me that I should not call any man impure or unclean.
Of course, Peter might mean there that God has shown him (or so he thinks) that he should not call any man impure or unclean simply for being of another nation or ethnic group. That would comport with his later statement of belief (reported in v.34) well enough.
On the other hand, the vision itself could be construed as universalistic in scope (though easily misunderstood as meaning something less).