At numerous points in the Harry Potter books it is made evident that Mr Weasley is somewhat...inexpert when it comes to his knowledge of the Muggle world (despite his inherent enthusiasm).

Mr. Weasley liked Harry to sit next to him at the dinner table so that he could bombard him with questions about life with Muggles, asking him to explain how things like plugs and the postal service worked.

“Fascinating!” he would say as Harry talked him through using a telephone. “Ingenious, really, how many ways Muggles have found of getting along without magic.”
_{(Chamber of Secrets, Chapter 4, At Flourish and Blotts).}

“You’ll be paying now, then?” said Mr. Roberts.

“Ah - right - certainly -” said Mr. Weasley. He retreated a short distance from the cottage and beckoned Harry toward him. “Help me, Harry,” he muttered, pulling a roll of Muggle money from his pocket and starting to peel the notes apart. “This one’s a - a - a ten? Ah yes, I see the little number on it now...So
this is a five?”

“A twenty,” Harry corrected him in an undertone, uncomfortably aware of Mr. Roberts trying to catch every word.

“Ah yes, so it is...I don’t know, these little bits of paper...”
_{(Goblet of Fire, Chapter 7, Bagman and Crouch).}

I've given some reasons elsewhere as to why this might be. What I didn't consider in that answer was the possibility that he could have taken Muggle Studies, which is offered as a subject at Hogwarts.

“What are you doing Muggle Studies for?” said Ron, rolling his eyes at Harry. “You’re Muggle-born! Your mum and dad are Muggles! You already know all about Muggles!”

“But it’ll be fascinating to study them from the wizarding point of view,” said Hermione earnestly.
_{(Prisoner of Azkaban, Chapter 4, The Leaky Cauldron).}

Of course, he's not completely clueless. Nevertheless, I would've thought that basic concepts like telephones and money would've been included on the Muggle Studies curriculum. Given his passion for all things Muggle I'd also have thought that Mr Weasley would have taken Muggle Studies if given the chance.

Is there any canon indication on whether Mr Weasley took Muggle Studies or not? If he did, why is he as ignorant as he is? If he didn't take it, why not?

As Bellatrix mentioned, there doesn't seem to be any evidence as to whether Mr. Weasley took Muggle Studies or not. However, I don't find it implausible that Mr. Weasley could have taken Muggle Studies and still be a bit of a duffer when it comes to Muggle things.

When Hermione explains why she's taking Muggle Studies, she says:

"But it will be fascinating to study them from the wizarding point of view

So there are different points of view that Muggle Studies can be studied from. I imagine that a Muggle teaching about a telephone would focus more on explaining how to use a telephone, while a wizard teaching about a telephone would focus more on why Muggles need telephones and what they use them for.

So someone taking a Muggle Studies class from a wizard might learn that because Muggles have no magical ways of communication, they have to use something called a telephone, which enables them to communicate with people not in their presence. But they likely would not learn how to use a telephone, as that would not be considered a particularly useful skill for a wizard to have (except for certain minority cases, in which the wizard could learn how to use it from some other source). Muggle Studies is more to help wizards understand Muggles than to help them be like Muggles.

This is perhaps supported by the fact that Hermione had to write an essay about why Muggles need electricity:

Harry looked around at the cluttered table, at the long Arithmancy essay on which the ink was still glistening, at the even longer Muggle Studies essay ("Explain why Muggles need Electricity") and at the rune translation Hermione was now poring over.

The above would be true of a reasonably good teacher. However, as we well know, Dumbledore does not seem to play such a hands-on role in what his staff are teaching, or how they teach it. Short of a teacher posing a clear danger to the students, Dumbledore might not interfere — even if the students were getting a bad education.

Here's how Muggle Studies as taught by Alecto Carrow was described by Neville:

We've all got to listen to her explain how Muggles are like animals, stupid and dirty, and how they drive wizards into hiding by being vicious toward them, and how the natural order is being re-established."

It is unlikely that any student in this class would emerge having any proper understanding of Muggle things. And while it is unlikely that even Dumbledore would stand for a teacher like Alecto, this doesn't preclude the possibility that an earlier Muggle studies teacher was incompetent in a different way.

In short, I think it is reasonable that taking Muggle Studies might not have given Mr. Weasley much useful knowledge of Muggle things. It may have helped him appreciate Muggles, and their world, in general but we should not be surprised that he does not understand how thinks like plugs, money, and the postal service work.

It's also possible that Mr. Weasley might have simply forgotten things that he had learned decades earlier, especially if he hadn't put that particular knowledge into use.

There’s no evidence about whether he did.

The only time that Muggle Studies is mentioned in reference to Arthur Weasley is when Percy is advising Harry on which subjects he might want to take, he tells Harry that Muggle Studies is particularly useful for wizards who work with Muggles, like his father. However, he doesn’t ever mention if his father actually did take Muggle Studies while at Hogwarts.

“People say Muggle Studies is a soft option, but I personally think wizards should have a thorough understanding of the non-magical community, particularly if they’re thinking of working in close contact with them – look at my father, he has to deal with Muggle business all the time. My brother Charlie was always more of an outdoor type, so he went for Care of Magical Creatures.”
_{^{- Harry Potter and the Chamber of Secrets, Chapter 14 (Cornelius Fudge)}}

Having an O.W.L. in Muggle Studies is mentioned as a qualification for liaising with Muggles when Harry got to look at possible careers in his fifth year, which may imply Arthur studied it but doesn’t necessarily mean he did. It may have been a recently added requirement, so may not have been in place when Arthur applied for his job. Also, he worked in the Misuse of Muggle Artefacts Office, not directly in Muggle Relations, so the requirement might not even apply to his field.

“She was poring over a bright pink and orange leaflet that was headed, ‘SO YOU THINK YOU’D LIKE TO WORK IN MUGGLE RELATIONS? You don’t seem to need many qualifications to liaise with Muggles; all they want is an O.W.L. in Muggle Studies: Much more important is your enthusiasm, patience and a good sense of fun!”
_{^{- Harry Potter and the Order of the Phoenix, Chapter 29 (Careers Advice)}}

So, there’s nothing that gives an indication whether or not Arthur Weasley took Muggle Studies. It’s not even clear that Muggle Studies was an option for Arthur Weasley when he was at Hogwarts, it’s not mentioned whether it was a course offered at the time he was attending. His lack of understanding of Muggle technology despite his interest in it seems to somewhat imply that he didn’t take Muggle Studies, since Muggle Studies covered subjects like electricity.

“Harry looked around at the cluttered table, at the long Arithmancy essay on which the ink was still glistening, at the even longer Muggle Studies essay (‘Explain why Muggles Need Electricity’) and at the Rune translation Hermione was now poring over.”
_{^{- Harry Potter and the Prisoner of Azkaban, Chapter 12 (The Patronus)}}

From what we know about Muggle Studies, it seems to provide accurate information - Hermione, who grew up around Muggles and wasn’t afraid to call classes like Divination nonsense, took it without complaining about its inaccuracies or wizards’ lack of knowledge on Muggle technology, and thought Ron should take it, which means she thought it’d be informative for him.

“I’ll fix it up with Mum and Dad, then I’ll call you. I know how to use a fellytone now –’

‘A telephone, Ron,’ said Hermione. ‘Honestly, you should take Muggle Studies next year …”
_{^{- Harry Potter and the Prisoner of Azkaban, Chapter 22 (Owl Post Again)}}

Since the class itself seems to provide accurate information, it doesn’t seem likely that Arthur Weasley could have taken it and yet remain so misinformed on Muggles, especially considering his interest in them.

In addition to Alex's answer, I would like to point out that not only is it not shown that the "Muggle Studies" subject taught anything practically about how Muggles use their inventions, but that the subject could well be full of errors, misconceptions, omissions, superstitions and hearsay.

Indeed, I imagine Hermione taking the subject for the pleasure of correcting the errors ... or perhaps for the guilty pleasure of letting them slide, much as you watch educational Youtube videos about your country or language which are made by foreigners.