Hi Niels,
December is the start of the dry season in Panama. If you will be doing most of your birding in the Canal Zone (Pipeline Road, Achiote Road, etc.) and other places near Panama City (Tocumen, Costa del Este, Cerro Azul), you won't need a 4x4. There are asphalt roads in good condition to all of these places. The same goes for El Valle.
You probably won't be able to reach the entrance to Sendero Los Quetzales (El Respingo) on the Cerro Punta side of Volcan Baru in Chiriqui. But your hotel will probably be able to get you a taxi to take you there. Forget about driving up to El Respingo unless you have a strong 4x4. I myself wouldn't tackle that one with a rental car. The Las Nubes entrance to La Amistad NP in Cerro Punta is easier to reach, a sedan with reasonable clearance should get you there (I've driven a Toyota Hiace van up there with 10 passengers!). Don't bother with Boquete, unless you're planning to visit Finca Lerida. Stay in Cerro Punta and walk the Sendero Los Quetzales all the way to Boquete. It's an incredibly beautiful hike! Your hotel should be able to arrange transportation back from Boquete to Cerro Punta.
Roads to and through Fortuna in Chiriqui should be no problem. I'm not sure how the road to Santa Fe NP is, I've never been there. The road to El Cope NP gets a bit rough near the end, but I've gotten up there in a Suzuki Vitara during the dry season. If you have other places in mind, let me know.
San Blas is another name for the semi-autonomous region of Kuna Yala. It consists of a large section of the Carribean coast to the east of Colon, where the Kuna live mostly on the islands. Some islands are a real tropical paradise like you see on the typical posters. If you want to do some birding in that part of the country, your only real options are Burbayar Lodge and the Kuna nature reserve in Nusagandi. I haven't visited either of these places, but some friends have and they say they're great. Only place in Panama to have a good shot at Xenornis! There are few birds on the islands besides the common shorebirds, it is more for your typical beach holiday and snorkling.
And don't worry about malaria. The chance of catching it is extremely small.
Let me know if you have any other questions. Also, there are a few Panamanians on this board, some of them professional bird guides (hi Guido, Venicio), who know a lot more than I do.
Regards,
Cedric