These are some suggestions from the University of Florida for dealing with Muscovy duck problems taken from the fact sheet Florida's Introduced Birds: Muscovy Duck (Cairina moschata): http://edis.ifas.ufl.edu/uw299

“Since many of the problems caused by Muscovies are the result of residents feeding these ducks, discouraging feeding in community parks and around lakes would help to alleviate some problems. In many areas, particularly in southern Florida, city ordinances ban residents from feeding ducks, although these rules are difficult to enforce. Efforts to decrease nesting success of Muscovies can also help to reduce populations. Eggs should not be removed, as the female will lay a replacement clutch. Instead, the eggs should be shaken vigorously (to render them unviable) and returned to the nest, or replaced with plastic eggs.”

Additional information from the Florida Fish and Wildlife Conservation Commission on some of the legal aspects of dealing with muscovies can be found here: http://myfwc.com/WildlifeHabitats/Duck_muscovy_ducks.htm  An excerpt: ”Muscovies are protected by Florida Statute 828.12 regarding animal cruelty. However, because these birds originated in Florida from domestic stock, they are not considered "wildlife." As of March 31st, 2010 a federal control order is in effect that allows control by landowners, wildlife management agencies, and tenants, agents, or employees without federal or state permits, and prohibits the release of muscovies.”

The above article also includes this: ”Muscovy ducks, like other domestic animals, are considered private property. If someone claims ownership, the birds are the owner's to do with as he or she pleases, so long as Florida Statute 828.12 regarding animal cruelty is not violated. Similarly, if the muscovies have no owner, no state or federal law prohibits their capture and humane euthanization. This can be a last resort to resolve a nuisance problem. “

See also this from the Florida Fish and Wildlife Conservation Commission:

http://myfwc.custhelp.com/cgi-bin/myfwc.cfg/php/enduser/std_adp.php?p_faqid=1904&p_created=1127834090&p_sid=Uz2vG6_j&p_accessibility=0&p_redirect=&p_srch=1&p_lva=&p_sp=cF9zcmNoPTEmcF9zb3J0X2J5PSZwX2dyaWRzb3J0PSZwX3Jvd19jbnQ9MzEsMzEmcF9wcm9kcz0mcF9jYXRzPSZwX3B2PSZwX2N2PSZwX3NlYXJjaF90eXBlPWFuc3dlcnMuc2VhcmNoX25sJnBfcGFnZT0xJnBfc2VhcmNoX3RleHQ9bXVzY292eQ!!&p_li=&p_topview=1