Have you read where uncorrected torticollis can cause learning disabilities later in life? Here's what I learned from my PT about what causes this. Google vestibulo-ocular reflex it or ask your doc / PT for more info. This REALLY motivated my husband and I to keep up on my daughters stretching.
Even when head "turning to side" corrects, it is super important to fully correct the "tilt". The tilt is related to something called "Vestibulo-ocular reflex". This reflex becomes ingrained at age 1, but up until age 1 it can be corrected (or so my PT says). This reflex is what can cause uncorrected torticollis to create learning disabilities later in childhood. The child with a slight 'tilt' sees the world at a very slight angle, so their perception of 'straight' or 'level' is off. This impacts things like reading (which is done on straight lines), writing, etc. It can also cause clumsiness.
More info: The vestibulo-ocular reflex (VOR) or oculovestibular reflex is a reflex eye movement that stabilizes images on the retina during head movement by producing an eye movement in the direction opposite to head movement, thus preserving the image on the center of the visual field. For example, when the head moves to the right, the eyes move to the left, and vice versa. Since slight head movement is present all the time, the VOR is very important for stabilizing vision: patients whose VOR is impaired find it difficult to read using print, because they cannot stabilize the eyes during small head tremors. The VOR does not depend on visual input and works even in total darkness or when the eyes are closed.