Incredibly useful website. I have a few suggestions but please don't take this as negative criticism! I travel a fair bit and having these things would make this website my "one stop shop" for travel needs!
* The ability to export a list of results into CSV or something else that I can import into a spreadsheet. I tend to make travel plans on spreadsheets, and this would be very helpful.
* Scrolling to the left or right makes the colours disappear? I think this may be an OSM limitation but it really confused me.
* Is there a way I can filter on multiple categories? I'd like to look at visa-free and visa-on-arrival in the same map.
* This may be personal preference, but the emoji are really distracting.
* The region filter doesn't seem to influence the subregion filter? If I select "Asia" as a region I assumed the sub-regions list would reflect only the sub-regions of Asia but that doesn't seem to be true
* If I can subscribe to visa status *changes* for my country by email I'd give up my email address immediately. I'd probably be willing to pay money for this if it's accurate :)* The fact that this is non-authoritative doesn't bother me at all. You may want to highlight this a bit more "strongly". Maybe give up some of that priceless above-the-fold real-estate just to save yourself any legal trouble.
* Consider linking to traveldoc.aero as well.
* Several people I know and work/travel with have multiple passports from countries that allow it. Consider allowing the multiple home countries!