Was there an animation mistake between 3:17 and 4:19 in the second episode?
After watching the whole season of the series and reading some other viewers' opinions (namely on MAL fora), I've come to believe this and other (one in particular I noticed, but others may have occurred) "errors" are actually intentional, because of the fact that the series makes use of different timelines as a plot device.  

On episode 10, for instance, we get to see the scene from the second episode once again, but this time the bow-tie does not change colours any time, being consistently orange:



On the scene shown on episode 2, the bow-tie colour change was actually accompanied by a rather "robotic" by the other characters. This was particularly noticeable on the exact moments the bow-tie changed colours. This other viewer suggests (on two different instances)that this was all done on purpose , so as to draw the viewer's attention to the "error" of the colour changing bow-tie (and of other particular scenes described on that post).  

On episode 10, there was another particularly noticeable "error":  



Notice how Yui's dress changes colours once she walks out the door. This viewer (incidentally, the same one from the other posts, though apparently more aggravated on this post) defends once again that this was all done on purpose, so as to show the viewer that several iterations have been made by Yui while trying to save Kaori (capitalisation from the original post, not me):  


  (...)YUI IS NOT TIME TRAVELING, SHE IS TRAVELING THROUGH MULTIPLE DIMENSIONS TRYING TO FIND THE COMBINATION THAT WILL SAVE KAORI. THE CHANGES IN DRESS (ALSO THE CHANGES IN HER TIE FROM THE SECOND EPISODE) WERE BOTH DONE ON PURPOSE TO SHOW THAT MULTIPLE ATTEMPTS HAVE BEEN MADE. THEY ARE NOT "MISTAKES" OR IN NEED OF QUALITY CONTROL. THEY ARE A CREATIVE WAY OF SHOWING THE VIEWER THAT WE ARE SEEING THE SAME EVENT FOR YUI OCCURRING MULTIPLE TIMES.  


So, after all this, I've come to believe those "errors" are actually intentional, as explained in all of the above. However, I have no official word on this.



There were, in contrast, some minor inconsistencies on the animation/drawing quality sometimes, and these ones are (most certainly) not intentional. I refer these only to have some comparison between what seem to be intentional and unintentional "errors". Here are some examples (the faces are poorly drawn on the first one, and the distance between the hands and the body completely off on the second one):