What I first noticed as a discrepancy and wrongly attributed as an animation mistake turned out to be foreshadowing of the three-year gap:
Taki's and Mitsuha's phone screens at around the 28:17 and 28:54 marks, showing September 12 as a Monday and a Thursday, respectively.
If we were to assume the time in Kimi no Na wa. corresponds to ours in real life, then we can reason that the only years in recent times in which September 12 was/will be a Thursday or a Monday are: 2011 (Monday), 2013 (Thursday), 2016 (Monday), 2019 (Thursday) and 2022 (Monday).
However you look at it, there is a three-year gap, except between 2011 and 2013, but we can rule that one out.
In fact, we can pinpoint the exact years (2013/2016) in the anime before the revelation of the time gap if we make the following observations:
- Taki's smartphone is an iPhone 6s in space gray, the only finish with a black faceplate.
iPhone 6s was first released on September 25, 2015.
- Mitsuha's smartphone is an iPhone 5s.
It could not have been an iPhone 5 as noted in the Kimi no Na wa. Official Visual Guide (page 110), due to the redesigned front camera and the new home button integrated with a Touch ID sensor that were first introduced with the iPhone 5s.
Either the props design was intentionally rough, or that after the release of the iPhone SE, Makoto Shinkai noticed its extreme similarity to the iPhone 5s and took advantage of it, as well as its convenient release date, March 31, 2016, to help mask the time gap.
He even went as far as giving Mitsuha a rose gold colored phone protector, which only became available as a finish since iPhone 6s, to further confuse us of the time Mitsuha was living in.
iPhone 5s was released in Japan on September 20, 2013, eight days after the September 12 screenshotted above (is that an oversight?) and almost three years before its doppelganger, the iPhone SE, would be released (that's a three-year time gap right there!).
- The only meteor confirmed to have resulted in a large number of casualties is the 2013 Chelyabinsk meteor, which, like in the movie, also split into two main fragments after the primary airburst disruption.
As a reminder, the fictional Itomori Accident occurred on October 4, 2013.
However, the first true hint was given much earlier, in the fascinating OP:
Notice here Taki suddenly grew taller while Mitsuha remained the same height.
Then in the 12-key-frames animation sequence that basically summarized the film, Makoto Shinkai is again playing tricks on us with the changing outfits, some of which are seasonal uniform switches, by pretending that Mitsuha also moved up in grades when in fact she did not.
According to Learn All About Japanese Girls’ School Uniforms and Become an Expert!,
Except for the warm season, girls usually wear sweaters or vests. Unless they have a school sweater or vest that they have to wear, they usually choose their own. The basic colors would be white, black, gray, and beige.
The sweaters are not part of the school uniform, but her own, as further supported by the three schoolmates who showed up for Mitsuha's confession each wearing a sweater of a different color.