When Cid first found Alpha, she had nothing on her, particularly clothes. Why did the bandits took the time stripping her when they knew they were just going to sell her anyway?
Possessed mutation has been noted to cause the body to grow and shift in unnatural ways that causes clothing to rip and tear apart. Rather than remove her clothes, her captors simply chose not to give her new ones after her turning into a lump of meat destroyed the first ones.
Bandits Killed Left and Right
Why didn't the Midgar Kingdom or the Order of Diabolos ever notice bandits were being slaughtered?
I think because it was just bandits they didn't care.
Well, Midgar Kingdom actually did. "Baldy" was specifically threatened to lose his domain if bandits problem won't be solved.
The threat of the Red Moon being underestimated
If the Red Moon was such a huge threat, why wasn't there more effective measures put in place in case it got out of hand?
Cid shooting himself in the foot
I don't understand this part during the Corporate Warfare arc. Cid/Shadow/John Smith discovers that the gold that he's been collecting for himself and Yukime is gone but didn't he know that Shadow Garden took them since he wrote a coded message to them what his plan really was?
Cid is working under the assumption that Beta and the rest of Shadow Garden will never be able to figure out his code, since it originated in another world (Japan, on Earth). In Volume 4 of the LN, we learn Japanese and the language of Cid's world are mutually unintelligible, and Cid starts freaking out when he realizes that Beta will eventually figure out that his code was based on written Japanese. He freaks out even MORE when Beta learns Japanese (although he observes that she speaks it rather badly). However, Beta never puts two and two together— she just assumes that it's all part of Shadow's "Shadow Knowledge" and all information is tied into some sort of "base code," which is how she figures out Japanese. That, and interacting with the trolls on Japan's post-apocalyptic version of 2chan.
Cid/Minoru's change in appearance
Cid, when he was Minoru, thinks he's acting as a mob character but in reality, he look super buff and everyone were just staring at him. When he was reincarnated, he made himself look skinny. Why the change if he thought his muscled form was the definition of being a mob character?
It was probably a choice made by the mangaka as some sort of visual joke. In both the WN and LN one of the issues Minoru had in his quest for power was his lack of size and Akane describes Minoru as someone who is "physically below average" and "an ordinary student who did not stand out", especially against the ex-military thugs who'd kidnapped Akane. They assess his height as "170cm... weight about 60 kg." Later on when Cid travels back to Earth, Akane dresses him in Minoru's old school uniform, and it fits the scrawny Cid/"Minoru" perfectly, to the point where Akane thinks she's seen a ghost and is brought to tears. There's no indication that Minoru was ever as jacked as depicted in the manga.
The mangaka HAS confirmed in a tweet that "Buff Minoru" was just something she added as a visual joke, and that she would feel guilty if it were to be included in the Anime adaptation that is currently in production.
The mangaka THEN doubled-down on the joke in the manga by having a "Skinny Minoru" attempt to fight the ex-military thugs, but once he realizes he's at his limit, he "gets serious" by Hulking Out into "Buff Minoru," complete with shredded clothing (except for his balaklava and magic underwear), with no explanation for his not-magical body transformation.
Once he reincarnates, he has magic, and thus no longer focuses as much on pure muscle strength to become a power in the shadows. Also the fact Cid thinks he can still be an ordinary mob character with a Heroic Build is another case of his bonkers Weirdness Censor kicking in, rather than something he did on purpose.
Epsilon's Origin Story contradicts Alpha's Story
Cid recounts that Alpha was personally collecting the Seven Shadows but in Epsilon's Flashback, she was rescued by Cid. Either Cid quickly forgotten that first meeting or he interpret Alpha introducing Epsilon first?
In the LN it's clarified that all Seven Shadows were personally healed, at least, by Shadow. However, in Delta's flashback it's shown that Alpha had to fetch Cid to help subdue/heal Delta. So maybe the same happened with Epsilon (well, not the "subdue" part).
A bit of common sense here - as far as Cid Kagenou is Unreliable Narrator, his misunderstanding lies on conclusions - not on hard facts. And when he says that "Alpha collecting the possessed like stray cats" - he means exactly that. Nothing about the cure. At all. Alpha scouts them and either Cid is delivered to the victims or vice versa.
