In order to get a sense for where to anticipate problems in pumpkin square and/or pie bakery, we must first know what a pumpkin square and/or pie actually is. Anyone? Anyone? That’s right: a custard. A very thick custard to be sure, but one that’s susceptible to all the same problems as, say a crème brûlée. Chief among these problems: overcooking, which leads to cracking and weeping. Too much heat causes the egg proteins in the pie — which are responsible for thickening it — to clench up into little balls, squeezing out the water in the filling. The result is a clumpy, grainy filling and sodden crust.
However the nice thing about a thick custard like pumpkin pie filling is that there is lots of stuff in it that helps keep it from curdling. Unlike a more delicate custard, in which the egg proteins are quite near to each other and wont to bunch up, pumpkin pie filling is chockablock with pumpkin pieces, fat and sugar. These bits of detritus dilute the proteins, preventing them from getting too tight a grip on one another (or the matrix as a whole). Thus an overcooked pumpkin pie is usually just a disaster as opposed to a catastrophe, though neither tastes very good with whipped cream.
Avoid these troubles by taking great care with it. Use a straight-sided vessel if possible, since the sloped sides of a pie plate invariably cause the outer edges to overcook and crack (this is one area in which a square has a big advantage over a pie, Mr. Hans). The newer “deep” pie plates are good for this, but of course so are tart pans and even rings, if you happen to have one around. Bake low and slow, checking frequently to see how jiggly the center of the pie still is, and remove it at once after the center stops sloshing.