I will answer this as if I knew nothing about the games and only watched those movies.
Here's a short list of plot-holes/nonsense:
The Hive
-At the beginning of the movie, the scientist guy tries to break the glass with an axe but it fails. Then why is there an axe in laboratory? Is it there for the researchers to kill each other?
Labs have fire axes.
-The commandos break in to mansion wearing gasmasks, and then before entering the laboratory (where there's more chance for aerial infection), they take off the gasmasks.
Virus's rarely survive long outside a host, so it's logical that the airbourne virus was dead by the time the team got in and the masks were more likely incase of resistence using, or requiring the use of tear gas.
-The black guy survived the laser trap once, and the could have done it again, but he didn't.
I take it you forgot the whole 'it then turned into a grid that filled the corridor and sliced him into cubes part.
-Later when they reopen the laser trap room, the corpses are missing. If the virus spreaded airborne then Alice and the other survivors alive would be zombies too. This scene simply doesn't make any sense.
The mssing bodies is a continuity error, and again, and the virus would have already expired.
Apocalypse
-How did Alice know there were people in the church?
All that gunfire was likely a big hint. She could also sense the infected, so would know there were lickers inside.
-Licker in the first movie mutated into a big monster after it ate the corpse of Spencer right?
Why don't the lickers here mutate when they fed upon the guy they killed in the church?
Only one ate him, so maybe that one wasn't there, or there simply wasn't enough time for it to occur in.
-Carlos got bitten by a zombie and he didn't turn into one. Rain in the first movie got bitten and injected the anti-virus yet she turned into a zombie.
That would be the major plot point Anitvirus they cured him with
-Major Cain says Dr. Ashford is very important to Umbrella and sent a team out to find Ashford's missing daughter. And the end of the movie Cain shot the doctor to make Alice fight Nemesis. If he was so important then why did he shoot him? If he was not important then why did they search for his daughter?
He did explain literral the next moment that it was to demonstrate he'd kill anyone, even a valueble asset, so he'd definitely kill Alice's friends if she didn't fight the Nemesis
Extinction
-Raccoon City was nuked in Apocalypse, then how did the T-virus become a world epidemic?
Because in this universe they didn't hand wave away an incredibly infectious, speies jumping virus that had infected that many creatures with one bomb.
Also we see people fleeing the city in the film. All it would take was for one person to have been bitten and it would have spread like wildfire.
Look at any modern epidemic, like swine flu or foot and mouth disease for real world examples of how hard disease is to contain.
-Dr. Isaacs says they need Alice's blood to create a cure. How did they clone her if they didn't have her blood/DNA? If they just need her blood for the cure, then why would they create thousands of clones for the cure?
Alice had been heavily experimented on, and the Racoon City facility it occured in was destroyed. Presumably they were having to work out each step again through trial and error.
-Alice turned against Umbrella in Apocalypse. Then why do they keep making clones of her without erasing her memory?
Maybe they couldn't. They couldn't with the real Alice afterall.
-Why did T-virus cause global warm up?
It didn't. While it did kill off most plant life, Alice was in the Nevada desert. Other places would have been just a wasteland.
-The world is destroyed according to the story. Then why does Umbrella keep making B.O.W-s (smart zombies in this case)?
Those were accidents, they meant to 'cure' the zombies aggresion. When it didn't work, Dr Isaacs decided to use them as B.O.W.s rather than just destroy them
Afterlife
-Alice attacked Umb Corp. Japanese HQ with ALL her clones and didn't leave backup somewhere else. That's smart.
We don't know it was all of them, and if it were, then maybe she felt she needed them all to make sure she won the battle. She also didn't plan on them all dying, obviously.
-Los Angeles is not a desert, while they explained in Extinction that the virus caused the environment to turn into wasteland.
Alice was wrong. Or some plants were immune to infection, and she didn't know.
-Why didn't Wesker use auto-pilot instead of giving a long speech to Alice and causing the plane to crash?
The Autopilot was on, that was what was saying "Pull Up! Terrain! Terrain!"
Mountains are just very tall.
-How did Alice survive the crash WITHOUT her powers?
We see the photonegativ flash at the crash site, indicating she had used her powers. They were being destroyed, not gone completely.
-Who is that axe-man in the movie?
Who was the Executioner/nemesis/tyrants in the game? It's not particularly relevant.
Given that it turns up after Aliice arrives, and there's an Umbrella facility ship floating offshore, it was likely a Tyrant Wesker dispatched to fetch her, or drive her out of the prison to him.
-How did the axe-man managed to sneak behind the survivors without anyone noticing him and kill the Asian guy?
They were all concentrating on the hole, presumably he's sneakier than he looks.
[/quote]-"Wesker:Chris and Claire Redfield. You've become quite an unconvenience for me!"...How they did they become an unconvenience for him if they just met him?[/quote]
A throw away line that's a nod to the games. In universe, he's just annoyed by them interrupting and surviving alongside Alice, when all he wanted was her