During the fountain sequence where Beth picks up the coins, she enters with a bottle of champagne in hand. After a drunken speech, she enters the fountain, looks up at the statue and motions that she has her eyes on it holding the bottle in her left hand. The bottle disappears when she turns around and places both hands on her hips. It reappears inexplicably on the edge of the fountain when she starts grabbing coins from the water.
Nick's character was famously struck by lightning while playing football for Syracuse University in a rain storm. Syracuse plays in a dome so he would not have been exposed to the weather, however he could have been playing an away game. It never said the game he was struck by lightning in was a home game at Syracuse.
When Beth eventually returns the coins to her stalkers she seems to know exactly which coin belongs to whom. However, this was never established throughout the movie. The only "coin" of whose owner she can be reasonably sure is Nick's poker chip (and even there she gets it wrong, because it was actually thrown into the fountain by Father Dino).
During the cab ride scene when Beth just arrived, the footage can be obviously seen sped up as the pedestrian on the left side of the screen is seen walking 3x then slowed down to 2x as the cab passed by.
Nick's apartment scene obviously a set. When Nick first takes Beth back to his apartment, his friend comes to his door with a six pack of beer. Twice Nick slams the door shut in his friend's face, and each time the door slams, the entire surrounding walls bend and shake.
The goof items below may give away important plot points.
Joan tells Beth that she (Beth) must be the one to physically put the coins back in the fountain for the spell to be broken (the reason why she can not just mail the coins to Rome). At the end of the movie, it is Nick, not Beth, who throws the poker chip in the fountain, but the spell on the priest is still broken.
One of the coins taken out of the fountain is a 1 euro coin (an inner copper-nickel part with an outer nickel brass part). When Beth returns the 1 euro coin to Antonio there is a CGI flashback of the coin being thrown in reverse into the fountain. The CGI coin is quite clearly a 2 euro coin (an inner nickel brass part with an outer copper-nickel part, the reverse of a 1 euro coin) and not his 1 euro coin.