"I'm using 'Asphalt Roads' along with 'Alien Biomes' and other mods and constantly get errors about missing tiles"
Factorio's limit for the number of different tile prototypes a game can use at a time is hard-coded. Currently this limit is 255 tiles. If you load multiple mods that add a lot of new tiles (like "Alien Biomes" and "Dectorio"), this might be a problem, as "Asphalt Roads" alone needs 65 free tile slots to work properly (assuming all tiles being enabled).
If you experience problems, please try disabling some of the markings in Asphalt roads' mod options. Disabling both double line road line markings, for example, will free up 24 slots. If other mods allow disabling some of their tiles, please consider using those options, too.
Unfortunately, the Factorio devs do not consider raising this limit in the foreseeable future, so a bit of tinkering is unavoidable.