I like that regex more, but there are still a few minor changes I would make.

while (<>){
    if(/
        (
            [0-3]?[0-9](?:th|st|nd|rd)?\s+    # Get day
            (?:            # Get month
                Jan(?:uary)?|Feb(?:ruary)?|Mar(?:ch)?|
                Apr(?:il)?|May|Jun(?:e)?|Jul(?:y)?|
                Aug(?:ust)?|Sep(?:tember)?|Oct(?:ober)?|
                Nov(?:ember)?|Dec(?:ember)?
            )\s+
            [0-9]{2,4}            # Get Year
        )
    /ix) {
    print "$1\n";
    }
}
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The (?:) things are just like normal ()'s except they don't capture to a variable, they just do grouping, helps the interpreter optimize the regex.

The {x,y} means require atleast x of the previous item, and at most y. For refrence you can also say {x} which means require x of them, or {x,} which means atleast x.
-Ted