English buffs -- Why is this joke funny?

Factual Questions
1

Ok, maybe it’s not, depending on your tastes, but why is it supposed to be? I’ve been wondering this ever since I saw Real Genius for the first time, years ago.

So, Mitch, the boy genius, is attending some sort of welcoming party at his new college, Pacific Tech, where he meets stodgy old Dean Meredith, who offers the new kid ‘a bit of advice’. Mitch readily accepts, whipping out his pad and pencil to jot down the veteran academician’s wisdom.

“Always…no, no…never…forget to check your references.”

Mitch, a bit perplexed, thanks the dean, and quickly takes his leave. Meredith turns to his wife and says,

“I think the young people enjoy it when I ‘get down’ verbally, don’t you?”

That’s it. So, from context, I guess it has something to do with style guidelines about positives and negatives, but I don’t quite know what. Hopefully someone will give me the straight dope on this wordplay.

2

Real Genius

It was funny because the old nerd thought he was cool. And even the young nerd could see he wasn’t.

3

Kinda makes you wonder how often the old boy told it backwards.

4

Remember the Old Steve Martin Joke? I think it was Dali Lama told him, “Always … no wait, it was NEVER…always keep a litter bag in your car.”

It’s an old joke–“I’m gonna convey a piece of sage and unforgettable wisdom…(which I myself can’t remember).”

5

OK folks, now explain:

“I filed it under ‘H’ – for Toy”

**?**
6

Perhaps I can clarify the OP:
By ‘joke’, I don’t mean the advice itself, but the notion that the prof thought he was ‘getting down verbally’.
The question is, in what way was he ‘getting down verbally’?

Small Clanger, that’s just a non-sequitor.

7

He thought he was “getting down” because he told a joke.

8

“Helen”?

9

The American Non-sequitur Society.

“We don’t make sense, but we do like pizza.”

10

A (swatting mosquitoes): Man, these things are really getting on my nerves.

B: I guess that’s why they call them “insects”.