There's Something About MaryGoofs
The film features two troubadours several times throughout the film. Though we can hear the vocals and accompanying guitar and drum lines, this music almost never matches what the drummer and guitarist are actually doing with their instruments on screen. This was intentional on the part of the filmmakers and meant to be humorous.
Crew or equipment visible
When Healy is trying to revive the dog, he pulls two wires out of the table lamp and taps them together to make sure there is power. Letting hot and neutral wires touch as Healy did would cause a short-circuit and blow the fuse or trip the main breaker, potentially shutting everything in the living room off, and preventing Healy from zapping the dog.
Incorrectly regarded as goofs
Tucker asks Pat if he designed the Estadio Olimpico in Santiago de Chile. Although there are six different soccer stadiums in Santiago, not a single one is called "Estadio Olimpico". Since Tucker was a fake, hadn't actually been to Chile, and sensed that Pat was a fake, he probably made it up to see what Pat's reaction would be.
When Ted is at the chiropractor after helping the older man move, the doctor says tenderness left of "L-7". There is no L-7. Parts of the vertebrae are labeled: C-1 to C-7, T-1 to T-12, and L-1 to L-5. However, the term "L7" is a slang term meaning "square", and this is most likely a subtle joke at the expense of Ted.
After Ted is attacked by the dog in Mary's apartment and slides across the floor, he attempts to crawl away from the dog. We then see the dog bite Ted's ankle and the next shot is Ted's fingernails scratching the hardwood floor as the dog drags him back. If you pay close attention, Ted's fingers slide past the scratches made by the crew before the shot ends.
In one of the flashback to 1985 scenes, as Mary and Ted stroll down the street, she rants about San Francisco 49'ers' quarterback Joe Montana being obscure and underrated, but insists he will surprise by taking his team to a SuperBowl. By 1985, Montana had already won two Superbowls with the 49'ers.