When Ross comes in after getting completely drenched by the rain, he's soaking wet in one scene then completely dry in the next, then damp in the next. His hair also changes throughout the entire scene.
When Julie arrives at Central Perk as she hugs Ross she can be seen looking directly at the camera.
In the opening scene, when Rachel is telling Monica and Phoebe about The Kiss, we can see the set lights reflected in the television behind her.
One of the items on Ross's list of Rachel's good qualities (which he is shouting out to her while on the balcony in the rain) is "...how great you are with Ben!" Ironically, in every subsequent story where Rachel is tasked with watching Ben [all the way to season 7], we learn that she knows nothing about babies, she holds Ben "like a bomb", and generally she has never been around babies since the time she was one.
Monica says that she's allergic to cat hair. However, in the episode before Ross is picking up cat toys from Monica that use to be for their cat.