Preparation goes a long way to create a great event. Start planning at least 3 months in advance. Do pre-hackathon meetups, where people already start brainstorming projects. On a wiki, have lists of data sources, resources to get started, links to the best tools, and example projects. In e-mails to registered participants get people excited and thinking ahead and perhaps contributing or voting up ideas on a project site.
All this will make your mix-and-matches easier, because the more people have a good idea of what their aims are at the hackathon, the easier it will be for others to join in and collaborate. Especially if you have hundreds of teams.
As to the actual format of the mix-and-match, I've seen it all as participant or as organiser, and there is no best way to do it. In smaller groups, post-it-note or chalkboard brainstorming works well to get people to agree on one idea. For larger events like yours you should have people there to challenge participants to use an API or dataset or device, solve a particular problem, work in a particular way. You could even have people hang up posters of what they plan to work on and let the crowd sift its way through. Or you could leave it completely open, just distribute people into groups and let them have at it, like at some dinner parties.
Closing thought: set your expectations well. Your sponsor must have a vision for the hackathon, otherwise they wouldn't sponsor it. Support them in making this vision clear to yourself and others involved in organisation, and finally make sure the participants are well aware of what they are there to do. Then put in an earnest effort into making the event great: be there, make sure people are having fun, build an atmosphere of empowerment and community, using whatever has worked best for you in the past (e.g. food, music, ambiance, geek toys, VIP visitors, ...).
And let us know how it goes! :)