If you go to the flu.gov website you can follow the link for information for both seasonal flu and h1n1 flu vaccines and special precautions for asthmatics. They do recommend getting both vaccines, and they do say NOT to use the flumist nasal spray for the seasonal flu vaccine.
Supposedly, the h1n1 is quicker to attack the respiratory system, so that would seem to be a concern for asthmatics.
If you choose to vaccinate, to avoid mercury make sure you get a version without thimerosal, I believe both the seasonal and h1n1 vaccines have versions with and without - you should be able to find more info about this on the website also. As for concerns about other junk they put in vaccines, make sure there is no adjuvant (I haven't looked into the seasonal, but the original plan for h1n1 in the US was to use a version without adjuvants - this may change as supplies run low!). Adjuvants are used to enhance the body's response to the vaccine, some of them are untested and/or previously unapproved in the US. Many vaccines require the adjuvants because there is not a good match between the vaccine and the organism causing the disease. With h1n1, there is a good match, so the adjuvant would just be used to allow them to vaccinate more people.
In short, if you decide to vaccinate, you want a vaccine (for either flu) with no thimerosal and no adjuvants.