Dialectal is the adjective corresponding to the noun dialect (and dialect refers to a a variety of a language peculiar to a particular region or group). Dialectical is a less common variant of the adjective dialectic, which relates to logical argumentation and contradictory forces. The word is often used synonymously with logic or philosophy. So the ic differentiating dialectal and dialectical makes a big difference.
Examples
Though dialectal is the standard adjective corresponding to dialect, dialectical is often used in its place (the reverse is rare)—for example:
Voice Actions was always uncannily good at interpreting input and transcribing messages, but … I wonder how well it’ll do at working with dialectical nuances. [Washington Post]
While most people know of [the verb “birth”] only in a dialectical sense (“Miss Scarlett, I don’t know nothing about birthing no babies!”), it was quite common in the Middle Ages. [Columbia Journalism Review]
And these writers use dialectic and dialectical in their standard senses (though keep in mind that dialectical is a less common variant of dialectic):
A careful observer of character vocal and physical rhythms, of dialectal and gestural markers, he gives us a picture of the real Americans he encountered. [Oregon Live]
They are kind of dialectical. They feed on each other. [transcribed in Forbes]
However, he stresses that there is a huge difference between slang and dialectal colloquialisms. [Scottish Daily Record]
[T]he pitmen prove themselves surprisingly fluent in dialectical debate. [New York Times]