Ross' memories about Rachel happen out of order. The incident with Paolo's cat happened after the night Ross and Rachel did laundry together, but is shown beforehand in the sequence.
When Phoebe gets her invitation she mentions that it is adorable that Ben addressed hers and you can see her entire address on the envelope. A few seconds later she is opening the envelope and only her name is on it.
A close-up of Rachel's invitation shows that Ross made it out to "Rachel Greene". Ross should have known that her last name doesn't have the final "e" and is spelled "Green".
There is no reason for Ross to pay postage to have the wedding invitations sent to the rest of the friends. He uses the post box outside Central Perk which has already been established as being less than 100 steps from the apartments. He could have saved time and money by dropping the mail off at their building.