Our JP's have had the applicant of an emergency detention to swear to the affidavit. If I am reading the statute correctly, there is no requirement that the application under §573.011 be sworn. The same is not true for §574.001 application. Am I missing something? I cannot find any caselaw on point. It appears that any adult can file an unsworn application for emergency detention and then the magistrate may issue a warrant. Any help would be appreciated.

You are correct that section 573.011 does not require a verified application. Nor does it prohibit one. Section 573.012(a) provides that the judge or magistrate must examine the application and may interview the applicant. I suppose that, in his or her examination of the application, the judge could insist upon verification -- if for no other reason that to supplant the need to personally interview the applicant. It would seem that the real issue is whether the JPs' requirement of verification causes any kind of statutory or practical problem. I don't see a substantial statutory problem, so the real focus should be on pragmatism.

JP's can administer oaths and are also 'ex officio notaries public'. So, there should be no practical problem to having the applicant, who they are interviewing anyway, swear.
And, really, shouldn't they swear? It's a deprivation of liberty and permitting it without sworn testimony seems like a bad idea, whether or not there is an argument that it is not statuorily required.