I spoke to Matt Mullenweg about this very issue a couple of days ago at WordCamp UK in Cardiff. He said it's not a problem with the WP core, and if you can't get pre 1969 dates displaying properly then it's to do with your host (he seemed aware of the talk around the issue).
Matt mentioned a Benjamin Franklin historical blog powered by WP which works fine, but I've been unable to find it. He also said it's OK to have dates going right back to year zero (pre-Jesus blogging might be a problem, he said).
My site, the Beatles Bible, isn't displaying pre-1969 dates properly either (see, for example http://www.beatlesbible.com/1965/01/). I used the MySQL query workaround detailed by Hallsofmontezuma in this thread: http://wordpress.org/support/topic/159409
It's not ideal, however, as it doesn't seem to allow data formatting (eg 20 January 1965, rather than 1965-01-20 22:00:18, which includes the time down to the second), and the breadcrumb trail is effectively useless (it displays today's date rather than January 1965).
I'll give my hosting company a shout and see if they can help.
Interestingly, http://core.trac.wordpress.org/ticket/2149 was recently closed - not because, as Matt claims, the problem is fixed, but because the patch was out of date. It seems odd, possibly unhelpful, to change the status to wontfix/closed rather than needs-patch or even fixed.