Yes, homophones and also homonyms can. Spelling errors occur frequently with them, even when the context is clear.
These are some other examples for Korean homophones (if we ignore the sound duration):
Some clever advertisers use these words intentionally. For example,
빛나는 사인이 있는가 하면 빚내는 사인이 있습니다
uses the homophones 빛내다 and 빚내다. Both 빛내는 (not 빛나는) and 빚내는 are pronounced as 빈내는.
Absol brought a great example for the numbers 2 and e.
The majority of Koreans, even Seoulites, actually do not speak in the standard Korean. They are not aware that the correct pronunciation of the number 2 is 이ː (Please note the symbol ː) because they do not care about a long syllable now. This is the main reason that people are unable to distinguish between 일을 (1을) and 이를 (2를). If the speaker cares about the standard Korean, she/he will pronounce 일을 and 이를 as 이를 and 이ː를, respectively, although the listener may not catch the difference.
Jihyung Kang mentioned a strategy to avoid the confusion using accents. I would say that there is another useful strategy. Taking the symbol # as the pause marker, we can pronounce 일을 and 이를 as 일#을 and 이(ː)#를, respectively. I use this way in everyday conversation.
Where pauses do not make any difference, I put either additional words or collocations instead to clarify what I mean. Using synonyms and paraphrases is a good solution, too. For example, I need to say
백색과 상반되는 흑색을 써라.
when the listener takes "흑색을 써라" as "흙색을 써라." For 삼 분의 일 and 삼 분의 이, we can use 약 삼십삼 퍼센트 and 약 육십칠 퍼센트 instead. There are still other ways to paraphrase 삼 분의 일 and 삼 분의 이.