More formal way of saying "There are a lot of grey areas"?

but, however

there is a lot of grey area

or there are many gray areas

First, I don't like "there is/are" in formal writing. Some call it passive voice--which is totally incorrect--but I dislike it because it is weak. If you want to simply rewrite "there are Xs", you can write a variation of "Xs exist". In your case, you might say "Grey areas abound in psychology because it is a young science..." I also don't like "a lot" in formal writing. Don't ask "a lot" to do the work for you. Cite examples of grey areas and describe their extent.

The application has ambiguity and uncertainty in various areas

There are a few areas of uncertainty.

There are a few areas that require clarification.

There is a plentiful amount of achromatic sections?