I have edited category_item.php so the Read More... link appears in the same div as the introtext. However I am wondering how I would get Read More... to appear on the bottom line of the introtext?

The introtext is within a <p></p> so currently the Read More... link appears beneath the introtext.

The <p> tags are inserted through your editor while adding the text for your K2 item. The only way you can get your readmore to stand right in the end of the introtext element is through CSS.
Try adding this to your template or k2.css whichever your template uses

div.catItemIntroText, div.catItemReadMore {display:inline;}

Yiota Ziaggou wrote: The <p> tags are inserted through your editor while adding the text for your K2 item.

Doh !!! It all comes flooding back now.

All one needs to do is go into the Global Configuration settings for JCE (or whatever Editor they are using) in the backend and switch Container Element & Enter Key to "No containers & linebreak".

Many thanks for jogging my memory.