Mr. Smith is more correct

Mr Smith is also commonly used and perfectly acceptable.

I don't think this has anything to do with BE vs AE.

BE generally: Mr Smith
AE generally: Mr. Smith

Actually I remember having learned (back at school) that Mr (without period) is used in BE whereas Mr. (with period) is used in AE...

Pedant's rule: no full stop after a contraction. “Contractions” are those abbreviations which contain both the first letter and the last letter of a word, e.g.

Mr – Mister
Dr – Doctor
St – Saint
Rd – Road

Other abbreviations always take a full stop:

Ed. - Editor
Prof. - Professor
U.N. - United Nations

It may be true that this rule is observed more often in the UK than in the USA. But it can't be a BE/AE difference, because I learnt the rule from an American after living in perfect ignorance of it for over 30 years .

Well, perhaps the rule has changed since I had business correspondence decades ago - we used a full stop after all abbreviations.

I was told at school to put a full stop after all abbreviations, too. I don't think my so-called "rule" is very well known on either side of the Atlantic, even to pedantic buggers like me.

In my school (UK) we learned your rule in #4, Steve.

Life is a bit short for this sort of discussion, but in BE usage, Mr is more correct, because the last letter of the abbreviated word (Master) is present. But frankly, who cares?

Steve (BE)'s rule is, more or less, the one I know as very traditional BE; I would guess it might be from one of the older editions of Fowler.

I've never known it to apply in AE, and as Steve says, many if not most modern BE speakers aren't aware of it. I would guess that those BE speakers who still use -ize in certain words would be the same ones who would still distinguish between abbreviations with a period and those without.

The rule in #2 and #3 is what most learners of English need to know, and in the case of 'Mr(.)' it's sufficient anyway.

@hm-us
That's probably about right. I follow the contractions rule, now that I know it, and I use -ize instead of -ise too. I didn't learn the latter at school either - I got it from an episode of Inspector Morse.

Just wanted to add this:

The American spell checker that I use at work always marks Mr without a '.' as a mistake. But I usually ignore that ;-) because it looks so much nicer without a period/full stop in the middle of a sentence.... *g*

Chicago Manual of Style (15th edition, 2003) in ch. 15.17 social titles schreibt: Ms. Mrs. Messrs. Mr. Dr.

Nur als Beleg für die, die hier bereits für einen AE/BE Unterschied plädiert haben. ;o)