The veil that Monica gives to Phoebe is not her own. Monica's veil was full length with a comb attachment; the one she gives to Phoebe is shorter with an Alice band headpiece.
Just after Ross says, "Oh relax. I didn't say the F-word," to the kids on the playground, what appears to be the edge of the set is visible for a moment in the bottom right corner of the screen.
After Monica says "you won't find any porn or cigarettes under the couch....", the camera cuts to Chandler and Laura, and right when Laura is in the lower right hand corner of the screen, she begins to reply but her mouth clearly does not match the words that she is heard saying.
As with all the work-centered story lines concerning Joey playing Dr. Drake Ramoray on "Days Of Our Lives", that soap opera films in California, yet Joey and his friends are living in NYC.
Laura, the adoption social worker, remembers sleeping with Joey, so Chandler and Monica claim not to know him. When a social worker evaluates a home with a view to recommending a couple for the adoption waiting list, she would start by reading their file - which includes the signed letter Joey wrote in The One Where Rachel's Sister Babysits (2003) praising Chandler and Monica.
When lamenting his break up with Charlie, Ross states to Rachel that Charlie is the only beautiful paleontologist in existence. But Ross dated Julie in season 2, and Cheryl in season 4, both of whom were beautiful paleontologists.
Ross implies that there are thirty different types of poisonous spiders. whilst may people would make this mistake, Ross is a scientist and is hugely interested in nature so he should know that these spiders would be regarded as venomous not poisonous due to the way they administer their toxins.
Monica and Chandler have placed out several books around the apartment, presumably to show off a cultural side to them to the social worker. One of the prominent books is "The Photo Book", published by Phaidon. Whilst being a highly cultural and popular book, it seems unlikely that Monica would place it out given it contains, amongst other images, photos from crime scenes and of nudes. Whilst not "porn", it seems like an oversight given the amount of times she mentions removing Chandler's porn so the social worker wouldn't see it.
Monica and Chandler naturally go to great lengths to make themselves as presentable as possible with the social worker so that she'll give them a favorable report. But it seems odd that the social worker, who is a rather prim and proper person herself, freely admits that on her first date with Joey she went back to his apartment and slept with him, which seems out of character for her.