Southern BrE speakers frequently comment upon AmE speakers' lack of the /j/ or 'y' sound in words like Tuesday and tune: BrE /tjun/ versus AmE /tun/ (= toon). The difference is found in many words with a coronal consonant followed by an /u/, including assume, new, duke, sue, due. The two dialects don't usually differ when it comes to the /ju/ sound in other phonetic contexts, as in use, huge and cute.
Since BrE is so /j/-ful, it often strikes me when the /j/ goes missing in some British pronunciations of American names. Twice this week, I heard the American director John Huston's name pronounced by BrE speakers without the /j/: /hustn/. Americans would pronounce his name as /hjustn/ (imagine the 'n' as a syllable--I'm too lazy to go after the phonetic symbols tonight)--and as far as I can find, that's how the Huston family now pronounces it too. (There was a slight discussion of this on the American Dialect Society list in 2003. The name was changed from Houghton by John Huston's father, Walter, but the Random House Webster's Unabridged Dictionary reportedly says that Huston is pronounced with the /j/.) Similarly, BrE speakers often call Houston, Texas /hustn/, but the American pronunciation has a /j/. (We can't take the British too much to task for incorrectly pronouncing Houston Street in New York City, since most non-New-Yorker Americans pronounce it incorrectly too. The first syllable is pronounced like house.)
I encountered another missing /j/ in a production of Angels in America: Millennium Approaches in Johannesburg some years ago. There I sat, enraptured by an excellent production of an incredible play, believing that the actors had been imported from the US, as their accents were impeccable. But then the Mormon characters started referring to the state of Ootah. (The actors also seemed to be allergic to the the in the AmE phrase in the hospital.) It didn't diminish the strength of the play, but it left no doubt that the actors were not American.
This all could lead to the hypothesis that there are only so many /j/s available to a dialect, and if they use them all up in words like Tuesday, they'll not have them for use elsewhere. (Similar things have been claimed for dialects that don't pronounce the /r/ in dear but find an /r/ to put at the end of idea.) But I think the real story, once again, is that the pronunciation of names is particularly difficult to master.