The first Terminator film takes place in May 1984. This film was made in 1991 but takes place in either 1994 or 1995, since John is supposed to be ten years old. On the police car monitor, the T-1000's search on John's background information showed his date of birth as February 1985. In order for him to be ten in the film, that would mean T2 would have to take place in 1995, since it takes place in the summer. But if that's the case, it contradicts the T-800's claim that it was sent back 35 years in time (it was sent from 2029), which would place the film in 1994.
Also, because Edward Furlong was thirteen at the time of filming and didn't look ten, they changed the character to be thirteen years old in T3. However, that would mean that the film took place in 1997, which is when Judgment Day occurs. This also generates problems with Sarah's age: Dr. Silberman refers to her in this film as a "twenty-nine year-old female." However, if John is thirteen, this would imply that Sarah was a mere fifteen years old in the original film (again, allowing nine months for John's birth), which is clearly incorrect. One could conceivably postulate that Silberman was referring to Sarah's age at the time of her admission to the hospital.
On the Terminator TV series, the first episode takes place in 1999, with all the events from this film described as happening two years earlier, supporting the theory that T2 takes place in 1997. However, there are further contradictions, as the show also mentions that Sarah gave up John to foster care in 1995 and that the events of T2 took place a couple of months later.
The only real argument against is that in this film they keep referencing the date "August 29th, 1997." If it took place in 1997, they would likely not keep repeating the year; they would simply say "of this year," or just the day and month. One could split the difference and say it takes place in late 1996, as at night time it appeared cold in some scenes, suggesting it was wintertime in L.A. Also, for argument's sake, it could be said that the events of the first three films altered the timelines for each time traveler. For example, Kyle Reese was sent back before the timeline was altered at all; all of his intel would have been from the original timeline, then the events of that film altered history slightly. Then, in T2, the events significantly altered history, causing Judgement Day to happen further in the future. (T3 was made in 2003, but it is unknown if that's when it takes place.)