Continuity mistake: Interior shots of Ivy's cafe show a window in the back wall of the kitchen, visible through the door to the dining area. Exterior shots of the building show only a plain stone wall where the window should be.
Continuity mistake: S51/E204: Billy and Lilly are hitting golf balls into a glass. Billy hits his ball into the glass and knocks the glass crooked. They never straighten out the glass, but when Lily hits her ball into it, it's straight again. (00:56:38 - 00:59:10)
Beyond the Farthest Star - S1-E1
Other mistake: When showing Scotty on the bridge, some of the frames show more of his body than others. In those frames, you can see that he lacks legs.