What is your problem?
I'm not insinuating there is no problem, but you need to change how you phrase the thing that's bothering you.
Based on your question and how it is phrased, if I were to ask you to tell me what your problem is, you would likely say something along the lines of:
My wife can be a bit absentminded.
That is not a problem. It is a complaint. You don't get to call someone else's actions a problem, nor can you judge their character and then somehow force them to agree with your assessment and change because you tell them to.
What you can call a problem, is the negative impact something has on you. And this is what I'm trying to get to. You can only address a problem that you encounter in your life.
A better explanation of the problem would be:
It is stressful for me to have to continually check up on my wife because she be making absentminded mistakes.
This is something you can address, because it's a concrete issue. It doesn't judge your wife, it simply states the undeniable fact that you feel uncomfortable having to doublecheck everything.
This is something you can work at together, and find agreeable solutions to. It's not up to me to tell you what that solution is, that's between you and your wife.
But for the sake of example, you could agree that your wife will take more care with avoiding dangerous situations (e.g. fire hazards), and you agree to not sweat the little things (if her phone's not charged, that's her problem).
This will always be a compromise
You cannot expect your wife to live life to your standards. She is an absentminded person, and she cannot (and should not) spend the rest of her life forcing herself to be what you want her to be instead.
Instead, you should focus on how to live with an absentminded person. Look for simple solutions, e.g. post it notes (e.g. next to the intercom, reminding her to open the door).
A practical example
Personally, my soon-to-be wife is similarly absentminded, but maybe not to the same degree. For example, she turns on the lights (and other electrical devices) everywhere but never turns any off. After years of asking her to not leave things on all the time, I've now resorted to checking the lights before I go to bed, and reminding her once in a while. Over time, she has gotten better at it.
For example, I don't get upset that she leaves some lights on, but when she leaves the fridge door open, I do remind her that she left it open. In this case, it's not just a matter of a minor electrical cost but rather the spoilage of a week's worth of groceries, which is a significant financial impact, big enough to prompt her to not make that mistake. I don't need to get upset, because she understands that it's not okay to leave the fridge door open.
She cannot prevent her absentmindedness and there's no point in me getting upset with something that she cannot change.
I don't get upset at it, because at the same time, I do things that annoy her, and she quietly works around those annoyances. Living together means making compromises, and working around each other's quirks.
If there are things that you cannot work with, you need to address it together and find a solution that works for the both of you.
But do take note that if you address every little thing you've listed in your question, it's going to become overbearing and you will be less successful than if you only address the most important parts, and learn to forgive and work around the unimportant parts of her absentmindedness.
Improvise. Adapt. Overcome.
Just some ideas that came to mind when reading your question.
She forgets to open the front door after buzzing the gate open for me when I leave my keys inside. She opens the gate and goes back to whatever she's doing despite the intercom being right next to the door. And I have to ring again so she comes and opens the door.
As mentioned before, a post-it note next to the intercom would do wonders. You can also just remind her when she answers the intercom.
She don't tighten the lids or caps on anything. Medicine, sauce bottles, jars, creams... We've lost numerous bottles of sauce and medicine because the cap is only lightly turned to the point it sticks but when you pull it out it falls and smashes on the floor.
If your issue is that things are falling because the lids are loose; you shouldn't be picking things up by the lid to begin with. Hold the bottle, not the lid, and you won't risk having it fall.
This isn't even necessarily always caused by your wife. Thermal variations can cause metal lids to expand and contract, which loosens the lid (also a good tip for when you can't open a jar: hot water on the lid).
I'm not saying that this is what's happening for you; but my point is that even if you didn't have an absentminded wife, it's still possible for lids to be looser than you left them. Don't hold things by their lids.
She trips over any and every thing on the floor. Including my feet, power cords, little tables....
Open spaces and walkways. Don't leave cables lying around.
If we're walking in the street and I trip and fall or cross the street she doesn't notice I'm not there until I yell to her or she turns around some 10 meters away.
Are you tripping and falling often enough that this is a recurring problem? One could argue that you're similarly clumsy since you just mentioned that your wife often trips over things.
Tell her when you cross the street. When I'm out walking with my fiancée, she is blind to non-verbal cues (e.g. me turning towards the street to cross it), even when this means she bumps into me. So I've adapted to telling her "crossing here" when I change direction.
She's used to it now and I can interject it in the middle of conversation and she'll follow suit. She's genuinely blind to non-verbal cues so it makes sense to then use verbal cues.
She doesn't plug in her phone in the charger all the way in and leaves it without checking that it's charging.
That sounds like her problem. If she gets upset that her phone isn't charged, she should've doublechecked the cable.
There are also wireless charging options available which would avoid the same issue. Assuming she puts the phone on the charging pad.
She doesn't put out her cigarette correctly in the ashtray and leave it smoldering and I have to put it out to keep the smoke from getting in my eyes.
Self extinguishing ashtrays exist. For a cheaper solution, put some water in the ashtray so that any butt that lands in it is extinguished.
She places the cups down flat on the counter after doing the dishes so they never dry out.
You can kindly and slowly help her change this habit. If she's willing to relearn it, it's simply a matter of reminding her (without getting upset) that she's forgotten it again.
This is a matter of relearning a habit. It takes time, and you can kindly act as a reminder for her until she's gotten used to it.
If a visual reminder helps, put a dishrack on the counter which reminds her to put the glasses in upside down. Or even a post-it note could do the trick.
I have to check everything in the house before going out to check the stove, the clothes iron, water heater, TV...
She forgot the stove on and put a plastic tray of cutlery after washing them and we got out, we're lucky it didn't start a fire.
I do agree that absentmindedness that causes hazards should be habits that she relearns. But you can't relearn a habit overnight, and if you approach it with a combative tone, you're preventing her from relearning the habit. You catch more flies with honey than vinegar.
Check up after her, and remind her if she's forgotten something. It helps if you get her to go and fix the problem (compared to you doing it for her), because the physical interaction will eventually become muscle memory to her.
Additionally, if it's not already the case: smoke detectors and a small fire extinguisher.
She banged her head on a kitchen shelf knocking it and everything on it smasking on the floor and we lost all our mason jars with all the food that was in them.
First of all, I wouldn't believe that someone would do this on purpose, or willfully negligently, so I'm not keen on attributing blame here.
I'm also quite surprised at how seemingly easy your shelf falls down from a nudge.
Secure your shelf. Add a railing to it. If all else fails, don't put your glassware high off the ground.