Some of these we do have an answer for, though some are mundane and lame.Two words:
Underground Path.
A few more, to clarify:
There is a notice!
...Uncouth Trainers have been holding
battles in the Underground Path.
Because of rising complaints by local
residents, the Underground Path has
been sealed indefinitely.
Signed, the Celadon Police
It's for the Underground Path connecting routes 7 and 8 (better known as the tunnel between Celadon City and Lavender Town(ish)) in Kanto, from GSC. What the actual FRIG was the point of having this notice there? There's a level gap in GSC, the second strongest trainer in the game has his strongest Pokémon at lvl. 58, whereas Red has his weakest at 73. The games direly lack grind-able trainers to level your Pokémon up to the par of Red's. This secret location would be the perfect spot to have such battles, as per promised on the flyer, but no. The location wasn't even coded into the game.
Pattern Bush is another location I'd like to whack the designers over the heads with. "They say the patterns hide a secret". Nope, they don't. The patterns appear completely random, there's no code or secret to it at all, it just apparently looks like a circuit board. With the (un-alterable) Altering Cave at the end of the same route, you would think Pattern Bush's supposed secret and Altering Cave were connected somehow, but no.
Speaking of the Sevii Islands, they were full of those. The "door blocked by crates" house in Seven Island (and its counterpart in Mossdeep City) were intriguing, there had to be something going on behind that door. Oh, wait, it does - in Japan only.
Also in Mossdeep, we had the Space Centre and the White Rock. Neither served any purpose, which I found deeply disappointing back when I put hundreds of hours into Sapphire and Emerald.
Also, I guess the Ghost Girl in Lumiose counts a lot, but I expect her story to be told via the inevitable Hoopa event, or at least in "Z/X2Y2". Same would go for Couriway Rail Station (why?), the hidden message in Lumiose Rail Station (what?), the inacessible power plants (they even had doors, for frig's sake!) and the inexplicable mention of a Lava Dome Pokémon in Jaune Plaza. Loads of unanswered questions, but we're pretty much guaranteed to get another game to answer them.
Last, I expected Bulbapedia to figure out the exact number of residents in Lumiose City any day now. It took them embarrasingly long for being the definite Wiki for all things Pokémon, and long remained a mystery, but it seems the final number is 416.
The Underground Pathway was never coded in because it just couldn't be. GSC is notorious for pushing the cartridge space, and thus a few spaces that were taken out in Kanto were just space saving measures that got some in-world explanation. Granted, maybe having it open up post Blue fight in HGSS would have been neat, but Red is surprisingly trivial if you know what you're doing, so maybe they thought it was unnecessary for the remakes?
Pattern Bush has been explained. It's the IC pattern for the GBA carts
Sometimes, those cryptic hints are just 4th wall breaks
The Couriway Rail station message seems to be a message from Past Sycamore to his future self, as he hints about your prize being hidden there when you beat him there. It's kinda sweet in a way.
But most of the not well explained mysteries in X and Y seem to tie to event mons/a next game. Also, I too hope we can do something with the White Rock in ORAS. Not the space center, so much. Because the logistics of that are almost unbelievable