Unfortunately, yes, there are a lot of missable side quests in Final Fantasy 16. However, all side quests in Final Fantasy 16 are clearly marked on the world map with green icons. As such, it's very hard to actually miss out on quests completely.
The only problem is that there are key points in the main story where side quests will be removed from the game if you haven't completed them. Indeed, the game is designed in a way that encourages you to pick up side quests as you go, making sure that they're ticked off before the next big story moment.
This becomes less of a problem in the latter half of the game, where you can freely move between locations and complete side quests at your own pace. That said, there are still some side quests that disappear after key story scenes, so again, it is best to mop up optional objectives as and when they appear if you don't want to miss anything.