Disabilities among the Norse pantheon are an interesting thing... the theories about Loki expressing PTSD symptoms after having birthed Slepnir, Höðr's blindness leading to Baldurs death... but the one that seems closest to the circumstances described is Hœnir.

Possibly another name for Villi, Hoenir is one of the three Gods described as the makers of mankind, who contributed the quality of reason to the process. Unfortunately, in giving his reason to the creation, he's presently left without it. He was then traded as a hostage to the Vanir after the Aesir / Vanir war and now spends much of his time hanging out near Mimir, on whom he relies to make all of his decisions.

Mimir, of course, now being little more than a head, probably relies on Hœnir's help to attend to many of his want's / needs.

Prometheus from Greek mythology has a younger brother named Epimetheus, a name which roughly means "after-thinker" (Prometheus being "before-thinker," who is depicted as being very intelligent and cunning). Epimetheus often makes mistakes and excuses due to his lack of planning; for example, when the two brothers are tasked with creating life on Earth, Epimetheus wastes all of the gifts - teeth, horns, claws, incredible strength, etc. - on the animals, which forces Prometheus to steal fire for humankind so they may survive. While not exactly "mentally challenged," he always acts without thinking and is typically a buffoon. He later marries Pandora and helps her open the box.

Hercules (Herakles) was both dim-witted and mad.

For madness, no need to look further than the fact that he kills his wife, kids and self. See Euripides Herakles and Seneca's Hercules Furens, which is Latin for "Mad Hercules."

For stupidity, check out this goofy little story in Livy I:

Hercules, after slaying Geryones, was driving off his wondrously beautiful cattle, when, close to the river Tiber, where he had swum across it with the herd before him, he found a green spot, where he could let the cattle rest and refresh themselves with the abundant grass; and being tired from his journey he lay down himself. [5] When he had there fallen into a deep sleep, for he was heavy with food and wine, a shepherd by the name of Cacus, who dwelt hard by and was insolent by reason of his strength, was struck with the beauty of the animals, and wished to drive them off as plunder. But if he had driven the herd into his cave, their tracks would have been enough to guide their owner to the place in his search; he therefore chose out those of the cattle that were most remarkable for their beauty, and turning them the other way, dragged them into the cave by their tails. [6] At daybreak Hercules awoke. Glancing over the herd, and perceiving that a part of their number was lacking, he proceeded to the nearest cave, in case there might be foot-prints leading into it. When he saw that they were all turned outward and yet did not lead to any other place, he was confused and bewildered, and made ready to drive his herd away from that uncanny spot.

Virgil tells the same story too; this passage is a from a little later in the myth. When he hears the cows but can't find them, he walks around the whole Aventine 3 times, and then resorts to just ripping into the side of the hill:

Hercules arrived in a tearing passion, turning his head

this way and that, scanning every approach, and gnashing

his teeth. Hot with rage, three times he circled the whole

Aventine Hill, three times he tried the stony doorway in vain,

three times he sank down, exhausted, in the valley.

A sharp pinnacle of flint, the rock shorn away

on every side, stood, tall to see, rising behind

the cave, a suitable place for vile birds to nest.

He shook it, where it lay, it’s ridge sloping towards the river

on the left, straining at it from the right, loosening its deepest

roots, and tearing it out, then suddenly hurling it away,

the highest heavens thundered with the blow,

the banks broke apart, and the terrified river recoiled

This example is purely a Roman tradition, but I can dig up something in Greek if you're really interested. It's hard to put a finger on the tone of these sorts of things, but I really think we're supposed to be laughing at him here, and his stupidity highlights his strength.

Some Greek/Roman myths of Dionysus/Bacchus depict him experiencing episodes of madness, which was appropriate since he was the god of madness. In addition, in The Frogs by Aristophanes he's portrayed as a buffoon who's protected from his stupidity by his much smarter slave.

Did your friend tell you anything about this god in particular? Any stories or anything like that?