Objects, you can refer to as 古い with impunity. But I have never once heard a person referred to as 古い, so for a long time I thought the word just didn't apply to people. Still, searching 古い男 on Google gets pictures of old men. I imagine it's probably best to refer to old people as something like おじいさん or 老人 if their age is relevant, though.
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To us native speakers, 「古{ふる}い男{おとこ}」 does not mean "an old man". This is why direct translation could be dangerous at times.
「古い男」 to us means "an old-fashioned man". In other words, it is synonymous to 「古いタイプの男」. Therefore, 「古い男」 does not necessarily have to be biologically old because it is his value system that matters here.
To refer to "an old man", we use 「老人{ろうじん}」、「年老{としお}いた男性{だんせい}」、「おじいさん」, etc.
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But I have never once heard a person referred to as 古い,
We use 古い also 新しい for a person not for describing his/her age but for describing his/her way/tendency of thinking.
As you know 古い is an adjective, and an adjective has two different ways of use as a predicative use and an attributive one.
An attributive use of 古い is already answered using the example with 古い男, so I'll answer 古い in a predicative use.
古い in 彼は古い means 彼の考え方は古い His way of thinking is obsolete/old-fashioned, while 彼は新しい means His way of thinking is novel/original/innovative/unconventional/audaciou/avant-garde.
Both ways of use of 古い could be used, but I think 彼は古い/新しい is used more than 彼は古い男/新しい男です.
EDIT
A good way to refer to "an old man" is お年寄｛としよ｝り like （車内{しゃない}では、）お年寄りに席｛せき｝を譲｛ゆず｝る to yield one's seat to an elderly person (on the train).
