Re: the film title "Two Weeks Notice"
An apostrophe is required, and not because 'Notice' belongs to 'Two Weeks'--it doesn't. The apostrophe is required because 'Two Weeks' is a genitive of measure. That is, 'Two Weeks' answers the question, "What's the measure of notice?"; e.g., three years' work experience (What's the measure of experience?), two hours' time (What's the measure of time?), etc. When in doubt, change it into a periphrastic construct:
EX: two weeks' notice => notice of two weeks
There are sources online, Click here, that use the film title 'Two Weeks Notice' as an example of ungrammaticality. There should be an apostrophe, but don't blame the speaker if it's left out.
The problem is not with the speaker per se, it's with genitives of measure: the apostrophe is not audible after [s] or [z], so if you don't hear it, how are you suppose to know you should write it in?
Re: an hotel
I agree with tdol. It's not the correct usage anymore. In addition, traditionally the rules, as they were taught in school--way back when--were as follows:
<h> is aspirated (i.e., fully audible) when it occurs in an accented syllable, so in that environment it's preceded by <a>:
EX: a hot day, a hearing dog, a 'How're you doing?' phrase, a hurtful grin, a hateful letter, a holiday package.
<h> is unaspirated (i.e., barely audible) when it occurs in an unaccented syllable, so in that environment it's preceded by <an>:
EX: an historian's dream, an historical reference, an hysterical man, an heredity code, an habitual liar.
But, today, and with regards to the words above like, hotel and historical, for example, the unaccented syllables (ho- and his-) carry the exact same stress as accented syllables hoe and his, respectively. So you see, stress being relative, a hotel actually follows the traditional rule, albiet in a modified form.
In short, if you pronounce hotel as [o]tel, without [h], then use "an", whereas if you pronounce hotel as [ho]tel, with [h], then use "a". That's the traditional rule, right?