although i do find it a bit silly that the cops, etc. ask a mystery writer to solve the murder for them.
I find it silly that the castaways didn't kill Gilligan and use his body to plug up the hole in the boat and go home. Gilligan would finally be useful in death when he never was in life, and the rest get to live happily ever after.
And the show doesn't go beyond the pilot.
Every series (even the more realistic ones) has some not so true to life elements as part of the premise. You have to decide up front if you're willing to just go with it and enjoy the ride or not. Despite finding the other characters likable, and being open to trying anything Jim Backus was in, I can't stand the Gilligan character and wish the show had used my first paragraph scenario. So I tend to skip past Gilligan's Island when I see it on TV. With Murder She Wrote, I'm willing to accept the premise, even the supposedly sillier aspects, and enjoy the ride. If you're finding Season 1 to be only "somewhat entertaining," you might want to move on to a different show, because that "silly" aspect you describe is present for the entire series.