As the four guys enter Kodiac Valley talking about Adam (John Cusack) breaking up with the "great white buffalo", in the rear window they start to pass an awning as the scene changes inside the Denali then goes back to looking out the rear you see them start to pass the same awning again.
When Nick Weber is in the hot tube with the groupie (allegedly in 1986) They're listening "Push It" from Salt-n-Pepa but this song wasn't released until March 9, 1987 and advanced into the Top 40 the week of December 26, 1987.
When Nick walks up to his band members for the 1st time in the hotel lobby area, the song "Smooth Up In Ya" by the Bulletboys is playing in the background. That song didn't come out until September 1988.
Snowboarding was developed in the United States in the 1960s, and the first USA National Snowboard race was held near Woodstock, Vermont in 1982, so it wouldn't have been odd to see one on the slops in 1986.
In the ski chalet scene when they first realize they went back in time, there's a brief shot of a Nintendo arcade machine. However the "New Super Mario Bros" logo is from the 2006 Nintendo DS game, and an arcade game with that title or logo was never released.
When the guys are skiing down the mountain, the Motley Crue song "Kickstart my heart" is the music playing. They supposedly went back to 1986 but that song did not come out until 1989 on the "Dr. Feelgood" album.
The song "Bizzare Love Triangle" is played at some point. This is ironic, considering it's off the New Order album, Substance 1987 - and as pointed out several other times here, they traveled back to 1986.
When the time travelers return to 1986, they discuss doing everything the same so as not to mess anything up in the future. One person says "If you step on a bug, the Internet won't be invented." The internet was already invented in 1986, but not widely known or used in public homes.
In the scene where the guys encounter the ski patrol for the first time. Jacob is pushed down and the Ski patrolman's hand radio clearly falls in the snow. In the next shot it's back in his chest pocket.
When Lou is in the hospital and the decision is made to go to Kodiak Valley, he pulls out his catheter. Liquid sprays onto his pillow and it is clearly damp. In the very next shot the pillow is completely dry.
When the time travelers return to 1986, they discuss doing everything the same so as not to mess anything up in the future. One person says "If you step on a bug, the Internet won't be invented." The Internet was already invented in 1986, but not widely known or used in public homes. Moreover, these guys are from 2010 and will not necessarily know - then and there - when exactly the Internet was invented, so it would not be out of character for them to think that in 1986 Internet still had to arrive. (Incorrectly regarded as a character error.)
Lou is seen betting on Denver against Cleveland in the 1986 AFC Championship Game. While the actual Broncos-Browns game did take place in January 1987, it could be reasonably referred to as the 1986 conference championship because it followed the 1986 regular season (for example, even though they won Super Bowl XX in January 1986, the champions of that year are always called the "1985 Chicago Bears").
It is stated at the beginning of the movie that Jacob is 20. Since he was conceived in 1986, that would put "present time" at 2006 or 2007. However, the hot tub is clearly set to "2010" when the guys return to the present.
At the start of the film when Jacob Can be seen playing a PC game for about two seconds you can clearly see the Windows Media Player 11 "play" buttons as they come up when a video is full screen and has the mouse over it.
Towards the end of the movie as the three guys are talking to Phil and he is handing them the map printout from Lougle, you can see two search options underneath the address search bar and the option for "Search the Web" is checked instead of "Search the Maps" option.
(at around 1h 02 mins) After the end of the scene where Jacob sees the repairman at the cigarette machine, the next scene opens with Nick still passed out and leaning against the side of a urinal. After Nick wakes up you can see a smudge of his makeup on the side of the urinal for the rest of that scene.
When the one armed bell boy assists in taking everyone's bags to the room when they first get there, when he reaches to grab the bags you can clearly see the outline of his arm, that supposedly doesn't exist, under his shirt.
The goof item below may give away important plot points.
Most of the movie's anachronisms have to do with the setting being too early, but here's one that's wrong because the 1986 setting is too late. If Lou stayed in 1986, he couldn't have joined Mötley Crüe in time to record "Home Sweet Home" with them and appear in its video; that track was on the band's 1985 album Theater of Pain and in heavy rotation on MTV by the start of 1986, with Vince Neil singing.