Here is an example of one of the things Sheldrake would change about science, the null hypothesis.
His posit of morphic resonance basically states that memory is inherit in nature. So when a certain shape, structure, behavior, ect has occurred many times, it becomes more likely to occur again. We each have fields, and those fields are based off previous fields. Similar fields are connected and resonate with each other. This offers an explanation for all sorts of phenomena like esp and precognition, such as knowing who is calling on the phone before you answer. He points to examples of these fields when we see a flock of birds move in perfect unison, or how a squirrel knows to gather nuts for the winter when he has never been through one. It's basically an expanded concept of collective memory to include consciousness.
But science looks at this hypothesis and see possible predictions. If the idea were happening, shouldn't we see chemical compounds being easier and easier to synthesize as their shapes enter into natures memory? Shouldn't things like puzzles and video games become easier to solve as the enter more and more into the collective consciousnesses? Mankind has been learning to ride a bike for a pretty long time now, how come it has not gotten any easier for children of today to learn than it was 100 years ago? How come every year there are a percentage of squirrels who do not gather food for winter and die?
Well this is where Sheldrake starts criticizing science. Somehow, asking these questions becomes being anchored in the materialistic paradigm. He feels no need to consider the null hypothesis. Yet, when he finds studies that seem to support the idea, he accepts them. Rats learning to run a maze better and better with each generation. Termites working together perfectly even though they are blind and separated by a steal plate. When it is pointed out that these studies are sloppy and flawed, it's back to the "science is outdated" rhetoric.
Sheldrake see evidence in anecdotal information. If someone feels compelled to stop their car and then a tree falls in front of them, it''s confirmation. If someone is thinking about their mother and then she calls, it's evidence. He makes no mention of the times when we think of someone and they do not call, or the times we stop our car and nothing happens. He glances over basic critical thinking concepts such as confirmation bias, he devalues scientific concepts like experimental protocol, and then when he isn't taken seriously he blames the system for not being as deluded as him.
Here is a paper that demonstrates what can happen when we ignore scientific protocols when doing science.
This paper shows a positive conclusion that listening to music about being old actually makes you physically younger. When you use methods such as Sheldrake's you can pretty much show a positive result for anything. So the idea that listening to music about being old will reverse your aging process has as much support as Sheldrake's interconectedness.