Everything in the movie regarding Paige's journey to the WWE takes place between 2010 and 2014, but the WWE logo shown is the modern straight lined logo that was introduced when the WWE Network went on the air in February 2014, but was not made the official logo of the company until after SummerSlam that same year. This whole time, they should've been showing the "scratch" logo that was the official logo from 2003 until then.
In the film, Paige is recruited to NXT in Orlando. But at the time Paige was actually signed, NXT didn't exist yet. WWE's developmental league was called FCW (Florida Championship Wrestling) and was based out of Tampa. NXT and the WWE performance center opened in Orlando well after Paige was first signed.
In the opening scene where Zak and Saraya are fighting over what to watch on TV, it's on a modern flat-panel Hi-Definition TV. The scene was in 2000, when most HD television sets were in cabinets similar to old rear projection TVs, and flat-panel TVs that existed then were as expensive as a small car. An expense a family running a struggling wrestling promotion would hardly be able to afford.
Zak is seen as a young child holding a cardboard version of the WWE championship, in what appears to be 2000 from the clip he's watching. However the belt he creates is the belt introduced in 2005. You can see from the clip he's watching The Rock is holding a totally different belt (the Attitude Era World Title belt used between 1998 - 2002).
The movie appears to speed past anything about Paige's time in NXT, or fail to mention that she was then-current NXT Women's Champion when she won the Diva's Championship the Raw after WrestleMania in 2014.