A Google Webmaster Help thread has one webmaster who is upset that Google lists the site under one domain and has the cache listed under a different domain. What this webmaster finds out is that Google not only has different domains with the same content but tons of different URLs with the same content.
Canonical issues across different domains or within the same domain name can cause many issues for Google and thus your rankings.
Pierre Far from Google shared some other examples, outside of the picture above. He then explained why this is an issue:
When our algorithms are confronted with such large-scale content duplication, they may end up making a canonicalization decision that may not be what you intended. The recommendation, which is also the way to fix this situation, is to have only one URL (called the "canonical URL") serve any bit of content. For example, you may wish to have all the news in German hosted only on the .de domain, the English pages on the .org site, and likewise for the different languages. If you pick the canonical URL, you would be sending a very strong signal to our algorithms about your preferred choice.
Pierre then sums it up with this line:
The key point about your sites' structure is that the multiple domains as you have configured them are, effectively, mirrors of each other, which sends conflicting signals to our algos. You'd need to change the structure such that each page is reachable through one URL (i.e. on one domain) only.
Canonical issues can be handled by Google, but good webmasters make sure it is handled for Google.
Forum discussion at Google Webmaster Help.