Is it inappropriate for an author to copy and paste from his/her original paper in an extension paper?
The answer depends on the relationship between the papers, and I'm not sure which applies based on the information in your question. In computer science, at least, there are two general cases:
The extension paper is the "extended journal version" of a previously published short-form work such as a conference paper, workshop paper, or extended abstract. In this case, the rule of thumb is typically at least 30% new material. The extended paper will often contain large chunks verbatim, as it is expected to supersede the original paper, rather than existing as a separate work.
The extension paper is a separate work: in this case, extensive reuse of material is self-plagiarism. Two exceptions: first, related work, methods, and definitional material may often be reused as long as it is appropriate to do so---the material should be appropriately customized to fit the new environment. If the author would just be paraphrasing for the sake of paraphrasing, though, it's not necessary. Second, introductory material may be partially shared, though it should be more heavily customized for the new context.
In all cases except for minor reuse of related work material, the extension paper must declare a clear and explicit relationship with the prior paper.
Note that many other fields do not have the notion of a "journal version" and thus have much stricter standards.
Publishers have concerns about this from a couple of directions.
Copyright. A publisher will generally not want to publish something without making sure that the copyright is clear. If you've previously published a paper and then recycle text from that earlier paper into the new paper you need to make sure that you have retained the copyright on the text. Chances are that if you published your previous paper with a main stream commercial publisher then you transferred the copyright to that publisher and don't have the right to publish the same text in a new paper.
Originality. Most publishers have policies that say they only publish original research papers. It's an editorial decision whether the new paper has enough original content to qualify as original research. Reusing the text of mathematical definitions and standard theorems is a gray area where some publishers are willing to allow some text recycling. If this is done, it's critical that the original source be properly cited or better yet that the material be treated as a quotation from the original work.
Most publishers now use software to automatically check all submissions before they're sent out for review. If there's a concern about old fashioned plagiarism or recycling of text ("self plagiarism"), then this is often dealt with before the paper is even sent out for review.
As a referee, I would note the recycling of text from the previous paper and then review the current paper and consider whether the new work is sufficiently original to merit publication. It will ultimately be up to the publisher to decide whether they're willing to deal with any liability for copyright violation that results from the text recycling.
The Committee on Publication Ethics (COPE) has some useful guidelines on text recycling:
http://publicationethics.org/text-recycling-guidelines