When Rachel asks Ross and Julie if they are getting a cat together, she's not wearing a necklace. The camera turns to Ross, then when it cuts back to Rachel, she has a necklace. Then, back to Ross, and she asks "both of you?", and then Rachel has no necklace.
As Rachel is about to walk out of the coffee shop, the necklace she was previously wearing can be seen dangling off the edge of her tray.
When Rachel walks out of the coffee shop with the tray in her hand, she walks back in and sets the tray on a table. However, when she turns to leave, the tray is nowhere to be seen. Actually, the tray contains a yellow mug, and in the wide shot, the mug is visible on the table, which would imply that the tray is still there.