Not sure what the solution is, but it may start with education (if we haven't screwed that up too much already).
There are indeed serious problems for science education which need to be solved.
The obvious problem is with the textbooks. Creationist battles over science curricula and textbooks continue -- the NCSE regularly posts news about such activity. Creationists have been pressuring textbook publishers since the 1920's to keep evolution out; even though they've been less successful since 1969, the pressure is still there.
Another part of that problem is the writers' scientific incompetence. Most textbooks are written by professional textbook writers, not by scientists. As a result, many falsehoods and misconceptions are included, causing the quality of the science in those textbooks to be appalling. Since the 1980's, scientists have become more involved in textbook selection (eg, California science textbook selection in the 1980's in which the state ended up approving a minimally-corrected textbook behind the scientists' backs -- I need to write a webpage about that). Also, scientists have taken to writing some of the textbooks themselves -- in the 1960's, it was the Biological Sciences Curriculum Study (BSCS) textbooks written scientists which placed Susan Epperson in violation of Arkansas' "monkey law" which led to the striking down of those laws in Epperson v. Arkansas (1968).
The second problem is that many secondary-grade science teachers lack competence in the subject matter and, as a result, end up teaching their own misconceptions to their students.
Many school districts cannot afford to hire teachers trained in science and instead press other teachers into service with the philosophy of "They know how to teach so they don't need to understand the subject matter." My younger son's first middle school science teacher was the home-ec teacher; he knew more than she did and was able to explain it better, so his fellow students kept coming to him for help. In the early 1990's, John Peloza was a high-school biology teacher who sued his school district for not allowing him to proselytize between classes (Peloza v. Capistrano School District). In his own schooling, he had taken the bare minimum number of biology classes. His bachelor degree was in Physical Education and his MS was in Education in which his thesis was about coaching softball. While teaching in a small school district (on Santa Catalina Island, as I recall), that PE teacher was assigned to teach biology.
Interesting historical note: John Scopes was a PE teacher whose appearance in the biology classroom was in order to serve as a test case for the ACLU. That attempt to get the "monkey laws" before the US Supreme Court failed when Scopes' conviction was overturned in the appeals court because of a legal technicality.