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 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.