Penetrating armor takes a lot of effort. Striking where the armor isn't is much more efficient, if you can do it.
While eyeslots were usually a very small target on a medieval helmet, an accurate or lucky thrust could penetrate them, with unpleasant consequences. Chastelain reports that when Jacques Lalaing fought Diego de Guzman at Valladolid, Lalaing “turned the lower point of his axe, and struck three blows, one after the other, within the eyeslots of Diego, in this way: he wounded him in three places in the face…the first stroke on the left eyebrow, the next on the bottom of the forehead on the right side, and the third beneath the right eye….”
Given the number of blows that penetrated Guzman’s eyeslot without hitting an eye, I suspect that Lalaing was deliberately choosing angles of attack that were likely to produce a bloody wound, but unlikely to blind his companion.
And having achieved the difficult task of penetrating his opponent's eyeslot, it's possible that his point never left it for the next two blows, instead pulling back only far enough to shift to a different aim point on Guzman's face.
Lalaing's achievement was a difficult one against an opponent who could move, dodge, defend and strike back. To the best of my knowledge, it was unique in recorded medieval foot combats.
Not everyone fought with a closed visor, which significantly impaired the wearer's ability to see and breath. Lalaing himself often fought with his face entirely or partially unprotected, and many of his contemporaries made the same choice in single combat. Of the ten foot combats at the Pass of the Fountain of Tears in 1450, four of Jaques de Lalaing's opponents fought with their face fully or partially exposed, four with their visor closed, and in two the accounts are ambiguous. Lalaing fought only one of these combats with a closed visor, a series of blows exchanged with the estoc, struck with three advancing steps and little opportunity to parry. For the other combats he wore a small round sallet without a visor and with a mail neck defense.
Sallets are very frequently shown worn in contemporary illustrations with a significant gap between the bevor and the lower edge of the sallet where the wearer’s nose can be seen. Even with the most protective version of the sallet, with eyeslots in the visor or skull, it is possible to wear the sallet pushed back so that the wearer looks out, not through the eyeslots but beneath the lower edge of the sallet. This can provide much better visibility than trying to see though the eyeslots, but the shape of the sallet protects the face from most cuts. In this position the wearer also has some ability to rotate his head from side to side: perhaps 15 degrees in each direction even if the bevor is attached to his breastplate. If the wearer wants more protection he can raise one hand and easily adjust the angle of the sallet so that the sallet overlaps the bevor, while using the eyeslots for vision.
The partially or completely exposed face presented a bigger target than the eyeslots, although still not a large one. At the Pass of the Fountain of Tears the combatants frequently tried to hit their opponent in the exposed face. Jean Pientois was wounded below his eye and Gerard de Rossilon was struck on the right cheek with a single handed thrust of the upper spike of Lalaing's axe. Chaselain reported that he was wounded, but de la Marche said that Rossilon threw his right hand in front of him so that he was hit but not wounded.
The numerous breaths that perforated the visor of the typical helmet intended for foot combat presented another point of vulnerability. In at least one case, the chronicler suggests that a very acute point might actually slip through the breaths far enough to injure the face. De la Marche reports that when Bernard de Bearn, Bastard de Foix fought the Lord of Haubourdin in a continuation of the Pas de la Pelerin of 1446, Bernard bore an axe with a lower spike that was “long and delicate, fashioned so that it might easily enter the holes of a basinet, and long enough to do great damage to the face of his companion”. This seems to have been unusual enough to draw comment. A very slender spike would be vulnerable to breakage. Probably Habourdin had visor holes that were small enough to exclude the typical robust pollaxe thrusting point, but vulnerable to the unusually acute point chosen by Bernard de Bearn. Habourdin seems to have been distinctly miffed by Bernard’s tactic. “When he was advised of the subtlety of the said axe, he said that he didn’t want to make his companion take pains to pierce the visor of his basinet. He quickly had his detached and entirely put aside, so that his face remained entirely uncovered.”
A point could slide beneath the mail aventail without piercing it, as in the 1381 joust with sharp lances reported by Froissart.
"At the first onset, Nicholas Clifford stuck with his spear Jean Boucmel on the upper part of his breast; but the point slid aside, and did not take on the the steel breastplate, and glanced upwards, sliding all the way beneath the camail, which was of good mail, and, entering his neck, cut the jugular vein, and passed quite through, breaking off at the shaft with the head; so that the truncheon remained in the neck of the squire, who was killed, as you may suppose."
This case happened by mischance and horrified Clifford, but Fiore dei Liberi, writing in the early 15th century, recommended an upward thrust beneath the mail and into the head as a deliberate tactic when you can strike at an opponent's back.
In certain hand positions it is possible to thrust at the palm of a gauntlet, protected only by thin leather, or inside the back of the cuff to strike the unprotected wrist. This is exactly what happened in Jaques de Lalaing's fight with Thomas Que, and Lalaing was so seriously injured injured in his arm that he was unable to hold his axe with that hand.
It's also possible to defeat body armor by stabbing up beneath it, as in this 1403 encounter at Valencia recorded by Monstrelet:
"Then Sir Jacqes de Montenay threw down his axe, and with one hand seized Sir Pere de Moncada by the lower edge of his lames. In the other he had a dagger with which he sought to wound him underneath."
The back of the knee and inside thigh were often unarmored, although difficult to hit if you weren't behind your target.
Lames overlapped, but a thrust at the right angle could force between them without piercing the metal.
Cabaret d'Orville in his work La Chronique du bon duc Loys de Bourbon, reported that in the combat between Châteaumorand and Cloppeton at Vannes in 1381, Cloppeton was wounded with the lance "between the lames and the piece" so that he fell and was carried off the field. It seems likely that the piece in this case was the breastplate, the largest piece of the body armor. The articulation between it and the lames that covered the belly would be a relatively weak point in the body armor.
Mail has justly been described as several thousand holes flying in close formation. Unless the inside diameter of the rings is unusually small, a very acute point can pass through the mesh far enough to draw blood without breaking a single ring.
This fits with Joinville's description of the aftermath of Mansurah in 1250. The previous day, he and his knights suffered under heavy Saracen missile attack. He counted himself lucky that he was only wounded in five places. He and his knights were still able to fight, but none of them could put on their hauberks. This exactly what one would expect from many shallow puncture wounds.