When Alan the student tells Ross that he's in love with him, Ross is in the middle of writing a "C" on the chalkboard that he messes up as he turns around. A few moments later, the "C" is missing without Ross erasing it. This is incorrectly regarded as a goof. The C with the tail is still on the chalkboard. It is merely an illusion that it disappeared caused by the lighting and camera angle on the chalkboard.
When Rachel and Joey leave for the awards, Rachel is wearing a pink coat. When they return from the award show, she is wearing a red shawl.
The "pink coat" was actually a bathrobe and when Rachel had it on she was still getting ready and wasn't dressed yet. She holds her make-up bag and has still socks on.