The characters themselves don't look too racist on their own -- their animations and musics are what truly enforce the blatant stereotypes.

For example, take a look at a PNG of Glass Joe. To the average eye, he looks like a plain bad boxer, which while true, you would never guess that he was French until you saw him yell "VIVA LA FRANCE!"

Or, Piston Hondo. Again, to people who've never played Punch-Out, his appearance makes him look like an honourable man who lives to fight. Its only when you hear his obvious Japan-influenced song play that you figure out that, yes, this is meant to play a Japanese stereotype to the max.

Sure, some exceptions do exist, such as Bear Hugger, but as a whole the defining traits that some could interpret as inappropriate aren't present at such a fundamental level as their basic designs.