Common Sense Note
Parents need to know that A Hard Day's Night is a great way to introduce kids to The Beatles -- or, as a family, to just enjoy their glory days. Aside from Paul's naughty grandfather, a lot of heavy smoking (typical of the era), and some brief drug-related humor (which kids may miss entirely), there's very little iffy content here, so just focus on singing along with the soundtrack.
Sexual
Content
A few bawdy jokes with a mention of an orgy and that Paul's grandpa is "sex obsessed."
Violence
Many fans trip while chasing The Beatles, and some others look faint in the audience later. A car is stolen, a dove is squished in a man's sleeve, a woman falls down a hole and is immediately rescued, some running from the police and talk of the mean things they can do to prisoners.
Language
One "damn."
Social
Behavior
By keeping things light and silly, fame isn't ever taken too seriously here, despite all the screaming, running fans. A few nice messages in the love songs, like "Money Can't Buy Me Love."
Consumerism
This movie is of course meant to sell the album as well. There are also brief glimpses of what looks like a Pepsi bottle and someone is reading a Mad magazine book.
Drugs / Tobacco /
Alcohol
Lots and lots of (era-accurate) smoking by everyone. Brief drug-related humor (John pretends to snort cocaine from the top of his Pepsi bottle). Lots of drinking at a dance club.