I came across this blog post which I found quite enlightening
About halfway down the article, the author gives examples and explanations of pairs of words which have different kanji but sound the same, and have a common meaning but also subtle differences e.g. 丸い vs 円い、生まれる vs 産まれる, 町 vs 街
He also gives recommendations for online (and physical) kanji synonym dictionaries. I like the look of the first of these in particular.