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 28:32 and 29:08, 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 Plus in space gray (the only finish with black faceplate). Notice the home button on the smartphones is unique to Apple's iPhones. iPhone 6s Plus was first released on September 25, 2015.
- Mitsuha's smartphone is a white iPhone 5 protected with a rose-gold-like color case. Makoto Shinkai is perhaps cunningly trying to deceive us into thinking that it is an iPhone SE, which has about the same dimensions (123.80 x 58.60 x 7.66 vs 123.80 x 58.60 x 7.60, units are in mm) and appearance (the power button is located on the top right of the phone in both models) as an iPhone 5. The first time we got a glimpse of Mitsuha's smartphone was in the previews 予告・特報2 uploaded on April 7, 2016, a week after the release of iPhone SE, so it was entirely possible that Makoto Shinkai, thinking on his feet or due to pure coincidence, took advantage of the similarities of the iPhone 5 and iPhone SE to mask the time gap by further encasing Mitsuha's iPhone in a protector in the rose gold color that only became available as a finish since iPhone 6s. iPhone 5 became available in Japan on September 21, 2012.
- The only meteor confirmed to have resulted in a large number of injuries 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 that Taki suddenly grew taller while Mitsuha remained the same height. Here, Makoto Shinkai is again playing tricks on us with the changing apparel (some of which are seasonal uniform switches) by pretending that Mitsuha also moved up in grades when in fact she did not. The sweaters are not part of the school uniform, but her own (see the "Sweaters and Vests" section of Everything you wanted to know about girls’ school uniforms in Japan, gray and beige would be the basic colors).