In season 9, Phoebe and Ursula's birthday is supposed to be in October, around Halloween because Phoebe has a birthday party and Joey complains about the fact that it's on Halloween. However, in season 1 their birthday is a little after Valentine's day when Rachel takes out the Christmas lights and hurts her foot.
When Monica returns to the nurse to ask for another form you can clearly see that she is using a pencil, so there was no need for Monica to get another form. However, this is not necessarily a goof. Monica might not have had an eraser or she probably didn't want [or rather the writers didn't want] the trouble and waste of [screen] time of erasing the whole form.
When the nurse calls and asks for "Monica" to inform her there is a mistake on the insurance form, Rachel gives the phone to Monica because they switched identities. When Monica picks up the phone, she identifies herself as Monica, though she was supposed to pretend she is Rachel. However, this is not a mistake on Monica's part. Since Rachel was using her insurance and the nurse couldn't actually see who was on the phone, Monica could "pretend" she is Monica as she would be more equipped to answer any questions. There was, however, a slight chance the nurse recognized her voice.
When Phoebe goes to see Ursula at Riff's, there's a shot of the outside of the café. You can clearly see the "Riff's" sign move as it's superimposed on top of the picture. There's a man that walks past the camera as well, and the sign can be clearly seen on him when he walks by.
At the final of this episode, when the gang "is speaking in Spanish", there are some errors in the subtitle, such as "a quien" instead of "y quién", "aviciedo" instead of "haber sido", "esiendo" instead of "haciendo".