Did I screw up my fan install?

Sorry, I'd have to disagree - anything with a flange that's secured to the trailer should have butyl tape between the flange and the surface to which it's being attached, and once that's done any potential entry point for water should be additionally sealed with lap sealant. Over time lap sealant loses it's resiliency, dries, and cracks and can't be relied upon for a waterproof seal, ergo the reason it's important to inspect and maintain on a regular basis. Under a flange how often do you think one would do that? ... NEVER being my answer, at least not until it starts leaking, which is obviously too late. Personally, I'd remove that vent and redo it properly.