You may not find this terribly rewarding unless you're included here, so this is a good time for casual and random browsers to turn back before they get too caught up in the sweep and majesty of the proceedings and can't let go.
The Nursing Madonna (Madonna Lactans)
The Nursing Madonna theme was first seen with the growing popularity of the iconography of the Virgin Mary in the 12th century, but it took off in the early 14th century, only declining after the Council of Trent's strictures in the mid-16th. But prior to the late 15th century, we've noticed, the artistic sense of human anatomy seems to have been very unreliable.
Jesus has long-range plans to save the World, but is presently engaged
(Lo Zoppo, Virgin and Infant surrounded by eight angels, 1455, in the Louvre in Paris) [viewed in 2012]
In Bologna, this is in the San Colombano church with its "Collezione Tagliavini di Strumenti Musicali" 
This can be found in the Chiesa Parrocchiale of St Mary Magdalene in Castiglione del Lago on Lake Trasimeno, attributed to the 'Sienese School', 14th century. 
Madonna and Child with St Stephen (with rocks on his head) and St Lucy (carrying her eyeballs on a plate, both with martyrs' palms), and with Baby Jesus nursing in an anatomically unsuitable manner (Jacques Iverny of Avignon, ca. 1425). In the Galleria Sabauda, Palazzo Reale, Torino. 
In the tympanum over the main door of the Cattedrale di San Rufino di Assisi -- the building was completed in 1253 -- with on the left, a Virgin Mary nursing Baby Jesus in an anatomically incorrect manner
Another anatomically challenged nursing in progress (by the Pseudo Jacopino di Francesca, early 14th century) in the Palazzo Ducale in Urbino [viewed in 2015]
A pleasant 'Nursing Madonna', ca. 1515, attributed to Goswin van der Weyden, grandson of Rogier van der Weyden, in the Basel Kunstmuseum
What's left of a Nursing Madonna picture in the Parrocchia Santa Maria della Verità (probably from a 14th century renovation, or possibly earlier), Viterbo 
That's about as awful as it gets; In the Castelvecchio or Castello Scaligero, Verona, this by a 'Veronese painter of the late 13th century'.
Another near miss -- by Michele Giambino, early/mid 15th century, also in the Castelvecchio, Verona
A detail of the 'Madonna of the Stars', by Marcello Fogolino, early 16th century, with unconvincing nursing arrangements; in Vicenza's Church of Santa Corona, begun by the local bishop in 1261 to house the relic of a genuine thorn from Christ's "crown of thorns" given to him by King Saint Louis IX as a thoughtful present.
Anonymous, ca. 1410, in the Palazzo Ducale, Mantua
Another badly damaged fresco; this has survived in the amazing 10th-11th century baptistry stuck onto the side of the Cattedrale di Santo Stefano or Duomo in Biella near Ivrea. 
A rather public occasion (Saints Peter, Catherine, Lucia, and Paul, and two determined donors), but at least the anatomical arrangements are all in order; labeled as by Bernardino Luini (ca. 1480-1532) in the pinacoteca in the Civic Museum of Padua.
-- Here, hold this for me. Nursing Madonna (called 'Madonna dell'Umiltà', by a 15th century local) in the Dominican Church of San Nicolò in Treviso [viewed 2017]
Still another Madonna and Child nursing scene with improbable anatomy, by the Dutch Gerard David or his circle, here called 'Rest on the flight to Egypt', ca. 1500+. In the Museu Nacional de Arte Antiga in Lisbon, Portugal.
More improbable anatomy, by an 'Unknown Netherlandish Master', ca. 1475-1500, also in the Museu Nacional de Arte Antiga
Somebody just wasn't paying attention; from the Museo di Stato in San Marino.
On the wall near the Via Roma in Vogogna, northern Italy
Hardly trying; this is in the Chiesa di San Giovanni Battista, Alba, Piemonte region
Another miscalculation; a fresco in the Castello Manta near Saluzzo, Piemonte 
An earnest attempt, in the fine Duomo di Asti, or Cattedrale di Santa Maria Assunta e San Gottardo
On a polyptych, apparently from the late 14th century, in the Palazzo Madama in Torino 
This cute scene by the workshop of Rogier van der Weyden (c.1465) just barely meets our standards for misplaced anatomy, but the little guy can join the crowd on the funny baby Jesus page. In the Art Institute of Chicago .