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However, MC has said twice recently that depth of crawl is dependent on PR (see his latest post regarding the Q&A seesion he got and the sitemap question)
As to why it goes down - there is obv. link rot and you may have to keep gaining links to keep level - also the Canonical and Hijack problem often results in PR disappearing :(.
With reference to different browsers showing different values - you are probably just hitting different DCs. PR on the DCs is not consistent currently.
The higher the Page Rank, the better the ranking of the new added pages.
When you have an high Page Rank you can concentrate just on content....
Lower Page Rank forces you to concentrate on page SEO, and link popularity to get the same results.
If nothing else calculating PR for all of Googles indexed pages is a colossal job. I doubt they'd do it if it didn't mean something.
The trick is not to get too hung up on PR for individual pages. I find the best way to think of it is like looking at a histogram from about 20 feet away. It is less about the tiny details and more about the overall picture it gives you.
Another good use of it is the disparity in PR across your site. Assuming most backlinks point to your homepage, it can be helpful to note the difference in PR as you move down your site. Many high ranking sites can have good PR for their homepage, with most of the others hovering around PR2. This is often the sign of a badly put together site. If you know what you're doing you shouldn't have to rely on this kind of thing, but if you don't it can be a useful early warning system that your site is badly linked internally, something that will adversly affect user experience as well as the way Google ranks your pages.
I am not sure whether this is good enough considering the short time this site has been around....
Also firefox shows a lesser PR for all the pages as compared with IE....what could be the reason for this?
IMO higher PR sites gets crawled more often and also deeper. The indexing time of new pages is also a matter and dropping to PR0 means start all over again on a new domain.
The calculation of PR is a complex matter but certainly inbound links (number and quality) is a key figure.
So yes PR really does help both in ranking and in quick frequent and deep spidering of your site. But compare it to others in your topic.
That said I do miss the days when I had a PR 7.