I'm about to add a sentence from a client onto a web page. I'm unsure which of these is correct. The first is his submission, and it sort of looks grammatically correct to my non-scholarly eye. Yet I would have used the second in conversation.
'We all have heard of the phrase, a picture paints a thousand words.' 'We have all heard of the phrase, a picture paints a thousand words.'

Terry, West Sussex, UK
I'm about to add a sentence from a client onto a web page. I'm unsure which of these is correct. ... phrase, a picture paints a thousand words.' 'We have all heard of the phrase, a picture paints a thousand words.'

Isn't this simply the infamous split infinitive? The first sentence avoids it. The second employs it.
Some teachers, pedants and editors insist that it's bad. Most of the rest of us think it a specious "rule" that can be safely ignored. As I just did.
My question about the sentence has nothing to do with it. Wouldn't both versions be improved by the deletion of the word "of" and the inclusion of quotation marks around the phrase "a picture paints a thousand words"? How can you "hear of" a phrase?
You can know it, you can hear it, but I'm not so sure you can hear of it.
I'm about to add a sentence from a client onto ... heard of the phrase, a picture paints a thousand words.'

Isn't this simply the infamous split infinitive?

No, it's the construction that's notoriously mistaken for a split infinitive. It's not unusual to see text in which an awkward construction has been used in order to avoid splitting an auxiliary verb from a participle, the writer having confused that construction with the split infinitive.

So far as I know, no respectable grammarian takes exception to splitting auxiliary verbs from participles. Some grammarians still object to splitting infinitives, but they're peeing into the wind.
The examples you've listed not only do not contain a split infinitive: They don't even contain an infinitive.
The first sentence avoids it. The second employs it. Some teachers, pedants and editors insist that it's bad. Most of the rest of us think it a specious "rule" that can be safely ignored. As I just did.

Again, there's no split infinitive there.
If you had said "It's a rule to safely ignore", that would have illustrated the split infinitive.
"He wanted to boldly go" has a split infinitive; "He had boldly gone" does not.
My question about the sentence has nothing to do with it. Wouldn't both versions be improved by the deletion of ... a phrase? You can know it, you can hear it, but I'm not so sure you can hear of it.

"Hear of it" is perfectly normal, idiomatic English.

If someone tells you "I understand there is a word 'resumal'", then you have heard of the word "resumal". If someone tells you "It's time for a resumal", then you have heard the word "resumal".
But the commonly used expression is "A picture is worth a thousand words". Until now, I've never heard or heard of "A picture paints a thousand words."
Actually, strictly speaking, there's no such thing as a "split infinitive" in English. In "to go", "go" is the infinitive while "to" is a particle that's often associated with an infinitive. But "infinitive" is widely used to refer to the expression "to go" itself, hence the
too-prevalent misnomer "split infinitive".
Students: Are you brave enough to let our tutors analyse your pronunciation?
To "hear of" a thing or a person sure. No problem.

But that's not my point. I was referring to its use in connection with a phrase or saying.
It seemed (and seems) unusual or illogical to me to hear *of* a saying.
If someone tells you "I understand there is a word 'resumal'", then you have heard of the word "resumal". If ... infinitive. But "infinitive" is widely used to refer to the expression "to go" itself, hence the too-prevalent misnomer "split infinitive".

I guess I boldly went, huh?
I'm about to add a sentence from a client onto a web page. I'm unsure which of these is correct. ... phrase, a picture paints a thousand words.' 'We have all heard of the phrase, a picture paints a thousand words.'

There is little reason to prefer either over the other, but I think better are
'We all have heard the phrase, a picture paints a thousand words.' and
'We have all heard the phrase, a picture paints a thousand words.'

You really do mean that we have heard the phrase, not that we have heard of it.
Again, there's no split infinitive there. "He wanted to boldly go" has a split infinitive; "He had boldly gone" does not.

Indeed not. For people who are bothered, Star Trek provides the standard and easily remembered example:-
"To boldly spilt infinitives no man has boldly spilt before." It's the 'to' that signals the infinitive here.
But the commonly used expression is "A picture is worth a thousand words". Until now, I've never heard or heard of "A picture paints a thousand words."

It occurs in this form in wimpy 70s song 'If' by Bread - the lyrics are at http://www.lyricsdepot.com/bread/if.html . A friend of mine who's a wine bar guitarist once did a gig where he memorably sang the next line as:-

"If a face could launch a thousand ships,
Then why can't I launch you?"
Telly Savales anyone?
DC
Students: We have free audio pronunciation exercises.
I'm about to add a sentence from a client onto ... heard of the phrase, a picture paints a thousand words.'

There is little reason to prefer either over the other, but I think better are 'We all have heard the ... a thousand words.' You really do mean that we have heard the phrase, not that we have heard of it.

Thanks. That's the one I've now published.

Terry, West Sussex, UK
It seemed (and seems) unusual or illogical to me to hear *of* a saying.

Me too; 'We all know* the phrase, a picture paints a thousand words' sounds much better, or at a push 'We've all heard the phrase, a picture paints a thousand words'. As it stands you might have *heard of* the phrase, but not be famialir with it; I've heard of The Marseillaise but I don't know the words. And, of course, as Bob points out, well no, we *don't all know that phrase. Like somebody said on the AUE thread, my reaction to the speaker would be 'bollocks, now I'm going to be singing that bloody Bread song to myself the rest of the day'.

DC