What is a word or idiom for a fellow who pretends to understand something, but doesn't. This person is fundamentally confused, and often goes to great lengths to convince others of their expertise and knowledge, but intellectually, really hasn't a clue.
The person is a poseur (or poser) with respect to understanding.
Noun: poseur pow'zur
A person who habitually pretends to be something he is not
You can use Charlatan.
a person who pretends to have skills or knowledge that they do not have.
You should also check out its synonyms and related idioms at the above link to see which one better suits your purpose.
In ancient Greek theater, there were three stock characters in comedy: the Eirôn , the Alazôn, and the Bomolochus. Of those three characters, the alazôn is closest to the person whom you are describing in your question as pretentious, clueless, confused, and boastful (see here, here, and here).
The alazôn is the boastful imposter who, in essence, claims to know more than he does (which is very little). Along comes the eirôn who bursts the alazôn's bubble by pretending to know less than he does (which is a great deal), a process which could fairly be called a humorous Socratic dialog.
Traditionally, a Socratic dialog is a means of getting at the truth of a matter by question and answer, question and answer. In a Greek comedy, however, the humorous interaction between eirôn and alazôn proceeds step by step until the alazôn is exposed as a phony. In effect, the eirôn skillfully and humorously causes the alazôn to paint himself into a corner.
If you are thinking of a real-life character whom you know personally, you might try being an eirôn to his or her alazôn. Simply, but skillfully, ask the person a series of questions which is designed to make the person squirm, and possibly even confess to his ignorance. In other words, make him feel ashamed for being such a pretentious braggart!
You could call him a mountebank. From Merriam-Webster online:
Mountebank derives from the Italian montimbanco, which was formed by combining the verb "montare" ("to mount"), the preposition "in" (converted to im, meaning "in" or "on"), and the noun "banco" ("bench"). Put these components together and you can deduce the literal origins of "mountebank" as someone mounted on a bench - the "bench" being the platform on which charlatans from the 16th and 17th centuries would stand to sell their phony medicines. Mountebanks often included various forms of light entertainment on stage in order to attract customers.
Later, extended uses of "mountebank" referred to someone who falsely claims to have knowledge about a particular subject or a person who simply pretends to be something he or she is not in order to gain attention.
As a side note, in Italian, montimbanco does no longer exist, and was replaced by saltimbanco (he who jumps on a bench), which primarily refers to the light entertainment on stage part.
Update: on second thoughts, you seem to focus on this person being confused - he's not intentionally trying to deceive but looks more like a victim of Dunning-Kruger effect . If it is so, then you're looking at a self-deceiver, or sometimes an impostor.
In slang, such a person is sometimes referred to as a head-nodder; I couldn't find a better reference than this.
An intellectual impostor. It's a two word compound, but this has the advantage of narrowing down the type of imposture. This was used in this review:
Suppose you are an intellectual impostor with nothing to say, but with strong ambitions to succeed in academic life, collect a coterie of reverent disciples and have students around the world anoint your pages with respectful yellow highlighter.
Richard Dawkins (1998/2007). Postmodernism disrobed. Nature 394:141–43
Intellectual faker is also sometimes employed, and may be nearer the associations you want.
Dunning-Kruger poster child. Or less cheekily, "victim of the Dunning-Kruger effect" which is a cognitive bias that prevents one from knowing just how incompetent and clueless one is, causing one to vastly overestimate one's knowledge and competence, pretty much the way you say.
I would point out one thing, though: You said "pretends to understand" but also "intellectually clueless" -- I think you meant "thinks they understand", because pretending implies they are aware of the situation (making their actions subterfuge), whereas true cluelessness, à la Dunning-Kruger or any number of great answers here, requires them to be unaware of it (making them guilty of, perhaps, lack of hubris and certainly of being annoying, but not of outright deception).
RationalWiki has some info on Dunning-Kruger, as do many other places on the Internet.
For a good time, listen to Act Two of this This American Life podcast, which features David Dunning himself.
Bullshitter or Bullshit artist
Perhaps a dilettante could work for you. Your definition is a little different, but in context means essentially the same thing. Dilettantes pretend they know lots even if they have little understanding.
a person having a superficial interest in an art or a branch of knowledge
Hypocrite would be the word I would use.
The word hypocrite is rooted in the Greek word hypokrites, which means “stage actor, pretender, dissembler.” So think of a hypocrite as a person who pretends to be a certain way, but really acts ... the total opposite.