Beginner here. I understand that Japanese has a large number of homophones, and that kanji help readers distinguish between them. Of course, kanji are not available in spoken Japanese. On the other hand, spoken Japanese has pitch accent. So, is there a significant difference in ambiguity between written and spoken Japanese? That is to say, are misunderstandings more common in one form or the other? And how do both compare with English?
You are right in that misunderstanding is common in spoken Japanese. but usually people who use Japanese know which word has ambiguity and escape the word or confirm the kanji of the word (like checking a spell).
I am not a native Japanese speaker, but used to speak it fluently. When I started to learn the language, I also worried much about many homophones which sounded same to me. Even though I knew native speakers had different accents for many of them, I was not able to learn everything and reading words with kanji was much more clear than listening to words that were spoken.
One thing very important to note in learning Japanese is just because there are many homophones doesn't necessarily mean they make spoken Japanese more confusing than other languages. All languages are understood based on context and the syntax (grammar), collocation (of words) and idioms are the factors that make any language more confusing than others.
Many English phrases and sentences are difficult to understand if you don't know the context. They could make you confused sometimes if you misunderstand the context. The same thing happens in Japanese, but I don't think Japanese spoken language is more difficult to understand than English or other languages that I know.
Don't worry so much about homophones. They will not bother you as much as onomatopoeia and mimetic words in Japanese.