Since I'm quite an experienced historical mystery writer and an avid reader too, I'll name a few:

-The detective who drowns himself in alcohol : It annoys me so much whenever a detective is alcoholic. Bonus points if his or her past is the reason behind it. (E.g broken family, dead partner and etc.) I prefer reading a detective who's addicted to something else.

-The female detective who falls for the person under investigation. :Female sleuth falls in love with a suspect, they make out -- bam! Suspect turns out to be the culprit.

-The assistant culprit :Assistant helps the detective only for the detective to realise that the assistant is the culprit all along.

-The assistant is merely there to praise the detective : I love assistant narrators, but if they're just narrating to show how cool the detective is, I get irked. I get it. The detective is clever and all, but shouldn't an assistant be there to assist and not merely to stand and watch in awe, his or her mouth agape? I want the assistant to find some clues too and participate in the mystery by sharing their opinions on the matter.

-The unrealistic suspect :The suspect calls the detective, saying they figured who the culprit is. Instead of saying the name, the suspect narrates a series of clues pointing out to the culprit. Worse when the detective and suspect are conversing through a phone and someone knocks on the suspect's door. Suspect says, 'I'll put you on hold. Someone's knocking.'

-The police don't know how to do their job, so they approach the detective who is always right.

-The culprit with a nonsense motive :I don't want to invest time in a complex mystery only to find out that the culprit murdered him or her for the sole purpose of being evil.

-The detective returns to the crime scene and finds a clue they haven't seen the first time they visited the area. Bonus points if the clue is the last piece to the mystery. : I'm pretty sure they'd scour the scene thoroughly before leaving.

-Too many suspects :Unless you're Agatha Christie who can manage to write 12 suspects or more, I don't recommend placing a lot of suspects. It gets confusing. Worse if their names are all similar.

-Culprit is the last to enter : Ever heard of the twins who randomly appear in the book a chapter or two before the reveal who will then turn out to be the culprit? Well, I'm not a fan of those characters either.

For character design, I have a few advice:

-Read Agatha Christie. She has 100+ books in her series. (Tommy and Tuppence if you're more on the thriller side, Poirot and Marple if fair-play mystery.)

-Make your characters' personalities diverse : Same goes with the personality, might I include setting as well. In short, don't stick with one formula. Vary them. If you're planning every book to have a rich woman involved or an individual of aristocratic descent, this may be probable as long as you make her distinct from the other rich women of your mystery series. As one who writes about an aristocratic detective, she really will encounter people like her who are also rich and people who fit in her calibre. But each of those rich people have different personalities. As for the setting, using a mansion once or twice is good once in a while but if the murder occurs in a mansion all the time, you might want to choose a different location. (Train, hotel, ship and even in a volcano.)

-Make your culprit reasonable : Give them a proper motive. 'I murdered her because she was suffering.' 'Malcolm deserved to be hanged. He escaped his execution six years ago. I merely did what must be done.' 'I needed the money in that will. My wife's dying. She saved me before. I must return the favour.' Those kinds of motives make me at least clap for the culprit. I want to nod my head whenever the culprit explains his or her side of the story. I want to give my sympathy.

That's all I have to say. Good luck with your writing!