Magnum makes a common mistake when he says he and Juliet are only committing trespassing and not breaking and entering. Trespassing occurred when they crossed the property line without permission of the owner. Contrary to what most people assume, "breaking" has nothing to do with breaking down a door or window before entering a building. This is because English common law was codified centuries ago when words had different meanings than today (the way it's sometimes a challenge to understand a line of Shakespearian dialog). Thus, if a person enters a building without the consent of the owner, even if he walks in through an open door, he is guilty of B&E. (However, it could be argued that Magnum knows this and is fibbing so as not to cause Greg any more stress.)
The will they - won't they romance has been a legit plot thread. Everyone knows they'll be together if the show runs long enough. Doubts are OK for these characters, but for Higgins to rush to an emergency session with her shrink over Thomas' gesture/overture is a betrayal of all the strength and self-confidence in her backstory and throughout the series. Higgins may have reservations, but she isn't that needy. Bad move.
Magnum grabs the gun, which was likely used in a crime and repeatedly touches it. He would know not to contaminate possible police evidence.