First of all, knowing pitch is not as simple as knowing the pitch on each word. There are many morphological endings that make pitch change on verbs and adjectives. For instance, taBEru becomes TAbete because -te will make the pitch shift to the 3rd mora from the end when the verb has pitch. Pitch also changes when 2 words or more form a new compound word (pitch is usually on the first mora of the second word). haYAi becomes HAyaku because -ku moves the pitch to the 3rd mora from the end. And so on.
It's true that different dialects have different pitch, but you have to understand that their pitch is part of a integral system -- if they say hashi with the opposite pitch, this is less likely to confuse the listener if the rest of the person's speech behaves the same way. In fact, there are even some rules that allow to predict dialectal differences.
I always tried to pay a lot of attention to pitch -- doing most of my research myself because it's very hard to find information at all -- and while I usually get it right, there are frequently times when I say a word out of context and I get confused looks until someone repeats the word with the right pitch. Almost everyone says it's not that important, and sure, it's not the end of the word if you get English stress wrong either, but in reality, it does frequently create confusion, and if you care about being understood well, I'd definitely pay attention to pitch.
Most Japanese people have no idea how pitch works because they've never thought about it. It's extremely difficult to find any information, and most dictionaries never mention pitch. But nevertheless, if you can find the right resources, pitch is worth the trouble.