When Paige and Emily are swimming in slow-mo and the music is playing (around 38:04), the camera is shooting from underwater and you can see both Paige and Emily, Emily in the foreground,and the lane lines are solid blue. In swimming, this means that they are within 5 meters of the wall on either side, and they're obviously towards the end of the first length of the pool because they surpassed the solid lane lines when they dove in, before they surfaced. The goof, however, is the next shot, shot above water, where Paige and Emily are now swimming where the lane lines are alternating colors, though they haven't yet turned around. This happens a few more times in the same scene with different shots.
During the swim meet scene, Emily's back is wet BEFORE she dives in for the relay, so you can tell that this is not the first shooting of the scene. In an actual swim meet, if a swimmer goes into the water before it's his/her turn to, the team would be automatically disqualified.
When Toby shows Spencer his ankle monitor, it is on top of his jeans. In reality, in order for the monitor to work, it would have to make contact with his skin.
When Hanna and Aria are in the library and Aria's parents leave, Aria says "Oh my god, my parents are having an affair with each other" but she isn't actually saying anything, she's mouthing something like "I know" or "Stop" to Hanna.
Toby says to Spencer, when she went to see him, that he could not leave his house for French tutoring, but in the last episode he was walking freely through the street.