One obvious issue is search engines. Search engines don't scan images as text, although they do consider the content of the 'alt' attribute to differing degrees when it comes to rankings. So, if the text is an important part of the content of the page that you want search engines to consider, you're always better off with plain text than with an image. Further, Google is also considering page load times in their ranking methods to a limited degree, and images are naturally much slower to load than the equivalent text as long as you're using a standard/common font family. Even if you choose a special font that has to be downloaded separately, there are ways of keeping the overhead within reason.
All that said, I wouldn't fault a designer for using an image to present some limited amounts of text if it was impossible or impractical to create the same effect with plain text and CSS. I'd just be heavily biased in favor of real text. In your case, I think you have to determine if the designer is using images as a tool or a crutch.