Rachel trusts Monica enough to run to her for help when she jilts Barry, but not enough to invite to the wedding in the first place. (Can you imagine the AIBU thread? 
)
Yet at the other end of the scale, Barry and Mindy invite Monica and Richard to their wedding when Monica knew neither of them before reconnecting with Rachel. Why? (Actually I do wonder if, both being medical professionals from the same town, Barry knows Richard and actually invited him plus one.)
Monica is a complete neat freak, yet has kitchen cupboards with no doors! They’re all full to the brim with crap! It would take Joey half an hour to put a couple of doors on for her, yet in ten years she never asks.
Phoebe says ‘My real dad ran out on us before I was born’, yet when she meets him, he talks about singing her a lullaby when she was a baby, which is where Phoebe got the melody for ‘Smelly Cat’.
Whilst not an inconsistency, Rachel’s career path is ridiculous. Becoming a buyer for a top fashion designer is bloody difficult even if you have a fashion degree and go straight into the sector. Going in at 28 when all you’ve done is been a bad waitress? It just doesn’t happen.
Ross meets Emily because Rachel is supposed to take her out on her boss’s behalf - her boss being Emily’s uncle. Yet there’s no sign of him at the wedding; and while Emily’s cousin chucks Ross out of his apartment because of the marriage collapse, Rachel suffers zero repercussions from being the indirect cause.