Answer: Yes it's good not to use "said" in every line of dialog and the way to avoid that is to use movement tags instead of speech tags, a method that was also explained in the "Common Mistakes" blog.
Stretching a point to find other synonyms for "said" draws too much attention to the words used, taking away from the meaning of what you've written. In this one case, it's better to use the same word over again, because readers see it so often they rarely pay attention to it beyond the sense of speech it conveys.
Using such words as commented, exclaimed, spoke, and so on burdens the meaning with the connotation of the individual words, rather than just the meaning, and can distract the reader's attention from what is said, which should be the important part of the information there.
All words have a dictionary meaning, or denotation, but many also have a meaning that accrues to the word in the mind of the reader and that is connotation. An illustration of the difference between denotation and connotation can be seen in the following two descriptive phrases of a man, with the same exact occupation:
A red-neck farmer.
A tiller of the rich, dark earth.