Revealing mistake: After the Kree arrive on the ship, in a side shot one of them opens the lunchbox holding the tesseract. We see the blue light emanating from inside, but that only appears once the box is fully open - while it's opening, there's no light inside at all, despite the tesseract always glowing. A later shot shows the glow being visible around the edges of the lid even when the box is completely shut, and when Carol opens it later, the glow appears immediately.
Other mistake: The fingerprint scanner in the room where Fury and Vers are detained is inconsistent. Fury tries it, and the scanning line moves quite fast before rejecting him with a red light. Vers tries it and there isn't a scanning line at all, it just flashes red. Then when using the fingerprint lifted from his ID, there's a much slower scanning line before it flashes green and unlocks.
Factual error: The internet cafe Vers visits runs a piece of software even more cutting edge than the brand new, still beta version of Windows 95; Netscape Navigator 4, a release from 1997 - certainly not 1995, when it still had very squared highly recognizable buttons and icons of a different color than those portrayed here. (00:35:15)
Factual error: When Minerva mistakenly picks up a NERF gun to shoot Carol, the blaster she picks up is a Sharpshooter II, released in 1995. The occupants of the station were supposed to have been stranded there for six years and could not logically have obtained this item.
Factual error: In the internet cafe, Vers searches for the name of the bar conveniently seen on the piece of machinery conveniently dropped by the Skrull. She can't google it, being 1995, so she uses Altavista. Props to the prop department for using the original logo of Altavista, but the URL appearing as result for the search is http://www.altavista.com/search etc, while it should have been http://www.altavista.digital.com, since Altavista in its early years did not own the altavista.com domain name.
Factual error: Everyone is gathered in front of Maria's computer waiting for the audio CD to load. Maria's computer is actually from the future, since it has installed not Windows 95 (beta or not) like in the internet cafe, but the even later Windows 2000 (telltale detail; the CD player program and the icon of the recycle bin). (01:05:45)
Other mistake: When Vers is using the payphone across from Blockbuster, the phone says it costs 25 cents for a call, but down below there is a big notice on the phone saying effective Nov. 1, 1995 the rate is going up to 25 cents. Trouble is it is June 1995, still five months before the rate change, and yet it already costs 25 cents. (00:25:40)
Other mistake: Vers saves Fury, blowing a hole in the ceiling and somehow getting to the upper floor (why she does not blast holes for the remaining floors as well is unclear). They should be then at -4 from the -5 they were in, but they are shown ascending a flight of stairs, at the top of which Coulson lets them enter the door for level -4.
Factual error: The calendar on the wall behind Fury when they are listening to the audio at Rambeau's house correctly lists the days for June 1995 (1st is a Thursday and 30th is a Friday), but the days for May and July are wrong (it shows May 1st on Sunday and last day as 30th on Tuesday, but 1st was Monday, and May has 31 days, not 30. It shows July 1st as Wednesday when it was actually Saturday, and the month of July only having 28 days). (01:05:00)
Factual error: In her second encounter with the Supreme Intelligence, Carol's memories 'jogged' by the Earth's sojourn include a record of "Come as you are" by Nirvana. A memory that Carol couldn't possibly have, having become Vers in 1989, and with the song being part of Nirvana's ultra-famous "Nevermind" album which came out in 1991. (01:27:30)
Plot hole: When Vers arrives at the bar, Nick Fury is already there. She went straight to the bar after stealing the bike, while Fury needed still to learn about the theft, link it to the case, with investigations taking place to maybe (only possibility that would not depend on the vehicle being reported) figure out that Pancho's was the destination from examining the search history of the browser. Fury went there by car. His boss also explicitly says to work on the case alone. Amazing he could be there with such timing.
Continuity mistake: Vers KOs the Skrull she does the warcry thing at, and then another one on the corridor steps. She is then seen fighting from the perspective of the corridor to her right, but there are no Skrulls in sight against that door, while at least one was already lying down there. There are two when the camera gets back closer, and when she neutralizes the last one who bounces onto his own stun mace, there are again two, and she somehow got between the last one and the others. (00:20:30)