There is no direct relationship between last-modified/expiry times and PageRank.
You should set up your cache-control in a manner that makes sense for your site's resources. Typically, this is a relatively long expiry time for static resources such as images, sound, and video files, and short time for new pages and scripts, pages which change a lot, and weekly or monthly promotions. As new resources mature, you can set the expiry times on static content to progressively-longer periods.
The benefits are that repeat visitors who have browser caching enabled (most) will see your pages load very fast, since only the most-often changed resources will need to be requested from your server. Even those without browser caching enabled will see some benefit, since your resources can be cached on the network - by their ISP, for example.
A second benefit of correctly-set expiry dates and last-modified headers is that SE spiders will be able to find out quickly whether your resources have been updated. This gives them more time to explore deeper in your site to find new pages/resources. While many spiders may not be this sophisticated, over time, the sites which are set up correctly are sure to benefit from anything that avoids wasting the spider's time - especially as the web continues to grow at an ever-increasing speed.
The other side of the question involves the benefit of updating and improving your pages frequently, striving to create and maintain useful, high-quality content. In many market segments, this can indeed lead to a PR boost, because other webmasters will notice your site's benefits to their users, and therefore will link to you in order to benefit their users. That can indeed give you a PR boost.
Also, PR isn't everything: PR only makes a difference in the SERPs when two sites are otherwise found to be an equally-good match for the search query. On-page optimization techniques and the link text used on incoming links control this aspect of ranking.
Setting up your server to provide correct cache-control headers is usually a simple exercise, has immediate benefits for your users, and may have a long-term benefit from the search engines. Good content will lead to an increase in PR over time. Why not take advantage of both techniques to make your site better?
caching tutorial [mnot.net]
cacheability tester [ircache.net]