Mobley was very politically motivated when he was working, and would prefer Grissom behave more like his day-time counterpart, Conrad Ecklie, who knows how to play politics (episode 109, "Unfriendly Skies").
Portia Richmond helped the Sheriff to get elected, and he wanted to close her case quickly, much to Grissom's annoyance (episode 115, "Table Stakes").
Grissom gets upset with Mobley, when he involved the FBI in the case of the day. So he removes Grissom. Mobley also offers Catherine the supervisor position when Grissom is put on forced leave for telling the press the case wasn't solved even though a suspect had been arrested, but she refuses (episode 123, "Strip Strangler").