IN: Which person is they?
The graduate students spend every waking moment studying for their classes since they offer much knowledge and tests as part of their itinerary.
OUT: their classes

IN: Which person is they?
The band connected well to their fans, so they continued to buy albums.
OUT: their fans

IN: Which person is they?
Amazon recently upstaged Gamestop on Battlefield 3 pre-orders because they lowered their price 30 percent below the competitor.
OUT: Amazon

IN: Which person is he?
Mark tackled the quarterback, but he was penalized.
OUT:
Mark