When Joey supposedly wins the Foosball game by scoring the final goal, the ball is clearly seen bouncing off the wall and back into the middle of the table.
When Rachel pulls her pants down to show everyone her tattoo, you can clearly see that she does not have a tattoo.
When Joey and Chandler are at the party, in the apartment that Joey eventually moves into, Joey mentions that there are mirrors on either side of the toilet. Later when Joey is showing the gang around his new apartment, he shows them the bathroom and it is remarkable for having a phone but there are no mirrors.
When Monica is decorating her Dad's birthday cake, the frosting changes between shots.
At about 0:16 (including commercials) in, a zoom-in, exterior Geller parents' house shot reveals their address number to be "170 05". It has been previously noted in the series that they live in Massapequa (on Long Island), New York. In this address number (with a space or a dash), the first digits indicate the cross street for ease of location. This specific denotation appears in Queens County (part of NYC), the next County to the West, NOT in Massapequa's Nassau County, NY.
Phoebe says 1922 was a long time ago "and then there was suffrage". In the USA, women received the full right to vote in 1920. However, it is well known that Phoebe gets her facts mixed up due to her traumatic and unusual upbringing. She is not meant to be correct in her facts as her comments are generally driven by her emotional responses to the subject matter at hand. All of the characters acknowledge her goofiness, love her and move on, it's part of the endearing charm of the character.
Rachel shows her tattoo: it is not covered by a plaster, the skin does not look wounded, clearly an old tattoo or a fake.