More around the part of the stairs close to the wall with you back facing the wall. As for the visual glitch go to the top floor, right before the ladder to the roof you will see a texture clearly not scaled correctly in relation to the other tiles(see attachment 1 for reference).

It seems that the player physics glitch happens sometimes when getting close to a ledge but you are blocked from falling by something, in this case a wall. Same glitch can occur when walking around the platform on the crane object, though not as often.