Adam Jr. is barfing all over himself while on the examining table waiting for the doctor. The others comment on the mess and the smell continuously. When the doctor arrives to administer the cure, the view from above shows him and the table perfectly clean.
When Lou takes the crew to go find Jacob (the two Smart cars pull up to the location), a couple walk past, both wearing blue shirts. As soon as Lou opens his door, it becomes a single guy walking while talking on his cellphone.
When Jill and Adam are talking on their video phone, we see the picture from the other side to Adam's point of view so it should be a mirror image, but it isn't.
The Smart cars were all electric (see the "e" on the rear sides of each car). Electric cars do not "rev" as they did in the movie when challenging/threatening characters.
A smart car only seats two people. There is not the physical space for three.
In the scene after Choozy Doozy, when they are in the street talking about parenting for dummies, Lou's arm tattoo becomes blurred.
All references to the years "2014" and "2024" were dubbed to "2015" and "2025" (It was originally supposed to be released Dec. 2014, but ultimately came out Feb. 2015)
When Lou and Nick are in the virtual reality world in Choosey Doozey they should appear to the world like the 2025 versions of their characters because it is the computer's representation of them to the TV-viewing audience, but in fact they look like their 2015 selves.
After Lou apologizes to the Smart car, the guys drive to Lou's place. When they exit the car, only Lou and Jacob get out. Nick is already standing behind the car, pretending to exit. The Smart car is a ForTwo model, and only fits two people. Hence the name. It also has no trunk space to speak of. It couldn't have transported all three guys together.
Nick is recording contemporary songs before the original performers get a chance to. This would only make sense if he had stayed in the past in the original film, or gone into the future at some point, but he has never done either of those.
Towards the ending of the film when "Lou" is apologizing to the "smart car", as the car is looking at him during the apology he's displayed as past Lou instead of future/present Lou.